Lego parts are incredibly precise, and the manufacturing tolerances have been consistent for decades. It's nearly impossible to replicate that precision on any modern printers.
That being said, different parts are more tolerant of wiggle room. Grabbing a stud is hard, grabbing a 2x4 is not. If you were going to print a minifig head, trying to replicate the neck barrel is gonna be tough, but making a larger hole with 2-3 ridges which taper to grip might be easier. If you plan what you're doing and are realistic about what you can print, it's definitely not out of the question.
Lego is ABS if I'm correct.