Simple Postgresql Statement - column name does not exists

Because "Smith" is an identifier, and in that position, an identifier is expected to be a column. What you probably meant is a string literal, which uses single quotes: 'Smith'. So

SELECT * FROM employee WHERE "lName" LIKE 'Smith'

You probably also want a wildcard in the string to search for ('Smith%'?). LIKE matching is anchored to the beginning and end of a string, unlike typical regular expression matching.

I would guess:

 SELECT * FROM employee WHERE "lName" LIKE 'Smith'

(note the different quotes; "foo" is a quoted identifier; 'foo' is a string literal)

Also, in most SQL dialects, a LIKE without a wildcard is equivalent to =; did you mean to include a wildcard?