Should I mention in my statement of purpose that I did not attend lectures in my last two years of undergrad?

I'd shorten and tone it down if I were you. Being a researcher involves a lot of sitting in other people's talks, so we all know that lectures are boring. But we still do it, because those are an excellent chance to socialize. We might just pack a paper to read in case it gets too boring. So your statement makes you look a bit like a loner. And being able to study something without being present in a lecture is a skill I'd assume anyone with a degree has. I don't think anyone ever finished a degree where all lecturers are perfect explainers and there is no need to study something on your own at some point.

So while I would not necessarily view your explanation negatively, I also don't see it as helping you much. So while you should explain your bad initial grades, I'd keep it short and simple. Something like "Coming from a non-academic family background I struggled initially, but then I changed my approach to studying" without going too much into detail.

Finally I think there is also a bit of an "I am very different"-undertone in what you write. It makes you seem aloof and possibly difficult to work with. This is again minor, but in direct comparison with a similar candidate it could tip the scales against you.

First, I am sympathetic to your dislike of sitting in classrooms, at scheduled times, for artificially limited intervals, and too-often lecturers/teachers who add little to the textbook, or even to their own notes... and are possibly non-interactive as well. Or, as in k-12 in the U.S., often far more concerned with crowd control (not their own fault) than course content.

So, when I got to college, I rarely went to class, but/and read assiduously outside of class. My repeated experiments with class attendance mostly confirmed my skepticism of the value of such attendance, with a few notable exceptions. And, from a pragmatic viewpoint, some instructors are very offended if one does not attend...

Thinking of the latter point especially, it would be hugely unwise to make a blanket declaration about the worthlessness of classes. It would also be wildly premature to claim that your viewpoint on that somehow validates your "research skills".

So, as in @mlk's answer, I'd recommend just saying that, due to being a first-gen college student, it took you some time to figure out how to successfully navigate the system, but/and now you are indeed succeeding.

Did your GPA improve as a direct result of not attending class?

Or did it improve as a direct result of you using the time you would have spent in class to do more study by yourself?

If so, the fact you didn't go to class is irrelevant.