How to deal with an inappropriate greeting in an email?

Personally, I would address it in a friendly way, but one that makes it clear that you think it's a bit of an odd form of greeting. It doesn't sound like it was intended in an unfriendly or disrespectful way (and I definitely wouldn't characterise it as sexist), but it does sound inappropriately overfamiliar (it would be a bit like one of my students starting an email to me with "Dude! ...").

The easiest way to deal with it, to my mind, is just to send a fairly normal-sounding (but obviously more formal) email back, and mention it in passing in a friendly way at the end. For example:

Dear <name>,

Many thanks for your email - really glad to hear that you've been learning a lot from the course. It's been good to see the improvements in your essay structure since the start of the course - I'm hoping that you'll be able to solidify those improvements over the next 8 weeks.

Kind regards,

<name>

p.s. Just a friendly piece of advice - whilst I'm not generally too fussy about people addressing me formally, I think I should probably steer you away from things like "my dear lass", not least because some people if addressed that way might take it the wrong way and get offended. I'm fine with people calling me by my first name (if the OP actually is), but I think that's stretching things too far.

I would simply reply:

Dear Student, thank you for your email -- I really appreciated it -- but in the future please avoid addressing professors in an unprofessional way, like "lass" or "lad".

I am sorry to add an answer to an already cluttered question, but I am worried that many of the answers are delivered by people that are outsiders to American academic culture and seem to have missed that the question concerns this.

American academic culture, while overtly low key in many ways, is most often very sensitive to people being addressed appropriately. It is also by now highly sensitized to the phenomenon of students not dealing with female faculty in parallel or equally respectful ways to male faculty. This is not the place to debate whether this is right or wrong (though I will reveal that I think it's right), but if you are not or have never been a graduate student or faculty member at an American institution, I think it is very likely that you do not properly appreciate how big a social error it is to treat female faculty in non-parallel ways and especially ways which could be construed as (i) overly familiar, (ii) belittling or (iii) sexual/romantic.

If you look at the dictionary definitions of "lass" (supplied in another answer), both of them are problematic by the above standards. Emphasizing the age or marital status of a female faculty member is overly familiar and/or belittling. Describing a female faculty member as a potential sweetheart would be seriously problematic: at many universities, this is in the ballpark of sexual harassment.

There is a good chance that the student chose the wrong words and does not mean anything ill, and I would also counsel the OP not to assume the worst. (Or rather, I would if I thought it necessary: as her comments make clear, it isn't.) However, let me be firm that the student has made a mistake that does require some correction, in part for the student's own good: similar behavior could be offensive to other faculty members, and more so to some, than it was to the OP.

I also feel the need to point out that some of the other answers are themselves not so respectful to the OP. More than one answer suggested that the OP book up on the denotations and connotations of "lass." But she is an English professor! Other answers suggest that she learn more about and/or be more understanding to the student's different cultural norms. But the student is an American man in his fifties and the OP is a 40-year-old woman teaching at an American university: I am pretty confident that she has met American men in their fifties, both in various English departments and in her real life. Why she has less expertise on this front than the posters here is far from clear to me. The word mansplaining comes to mind.

Bottom line: the student is not behaving properly, and the OP should certainly correct in some way. Doing so in a way that is understanding of the fact that the student is a probably-not-evil human being is, of course, wise, but she certainly doesn't need to take any lessons in male culture.

I myself would recommend responding promptly and crisply: just tell the student how faculty at American institutions like to be addressed: as Dr. X or Professor X. It could be two lines in your email reply. If there are any further issues, you can take them as they come, but in my experience students are generally very receptive to being educated about academic culture by faculty: they know very well how little they know, and (as usual?) faculty tend to assume that students know much more than they do.

Added Later: A lot of the discussion here seems to concern whether the student has essentially good intentions. So here is a remark that I sincerely (if naively?) hope will be helpful, possibly critical. Whether the student has (in some sense, any sense or all senses) good intentions is not relevant -- not relevant either way, I mean.

In my professional opinion as a tenured American academic with my fair share of administrative/supervisory experience and responsibilities: the OP's original characterization of the email as containing a "sexist greeting" is factually correct. By that I mean that the student used language that the culture of her institution would, if consulted, formally deem inappropriately disrespectful towards women. But here's a crucial clarification: in "sexist greeting," sexist is not a noun -- it's an adjective modifying greeting.

To take a step back for context, let me phrase it this way: the problem is not that the student is a jerk. In fact, this is doubly not the problem. On the one hand, the student could very well not be a jerk and still say or do inappropriate (by the standard of American university culture) things. Some words and actions are inappropriate even if the person saying them has the best of intentions. In my personal opinion, most of the time that students say or do inappropriate things, they do them out of ignorance or some other reason than ill intent of any kind. On the other hand: from the university's perspective, a student who is a jerk is still entitled to full service, so long as he refrains from inappropriate words and actions. I have taught (just) a few students who really are jerks -- dishonest, bigoted, or otherwise distressingly wrong-thinking. That makes things hard for me, because I have to teach them anyway, and indeed I have to be very careful not to allow my personal perceptions of their jerkiness influence my treatment of them in the course. If I witness a student making a sexist greeting and ding him for it in his course grade, he can appeal the grade, and neither "He is a sexist!" or "He wrote a sexist greeting!" will hold up as a defense.

So if (as I hope she does) the OP makes the student aware of the inappropriateness of his choice of words, she is not accusing him of being a sexist (of course there is no need for her to use the word "sexist" in any form when discussing this with the student; no one here has contemplated doing so, including her); rather she is identifying inappropriate behavior and informing him about appropriate behavior. (As I said in my answer above: I think that doing the latter is sufficient, as it implicitly accomplishes the former.) Is this one sexist greeting part of a larger pattern of inappropriate behavior, possibly one that could constitute harassment of the OP? Of course, I don't know, but given that the student and the instructor have already completed a whole course and seem to be largely satisfied with each other, I see no cause for alarm about that. And certainly the OP need not worry or hesitate about the appropriateness of responding to the student as suggested above: as a few people have already pointed out, she is literally getting paid to teach this student how to develop his writing. There is no way she can get in trouble for this.