I have a lazy eye. Should I go to an ophthalmologist or to an optometrist?

Ophthalmologist. An ophthalmologist can better treat lazy eyes or crooked eyes. A person who may need glasses or contact lenses for nearsightedness, farsightedness, astigmatism, or presbyopia (need reading glasses), but otherwise has no eye symptoms, can see an optometrist (a non-medical doctor). Ophthalmologists are medical eye doctors who do eye surgeries, treat eye diseases, prescribe medications, etc...
An ophthalmologist. An ophthalmologist can provide both medical and surgical treatments.
Depends on age. A lazy eye is one not seeing well usually due to childhood issues which are termed amblyopia. The "lazy" eye, due to poorer central vision turns in or out at times and sometimes always. Either specialty can provide optimum eye glasses but if you have concerns about the cosmetics of the eye position, you will need an ophthalmologist as he is the only one that can do surgery to straighten eyes.
Ophthalmologist. If you are interested in surgical correction go see ophthalmologist.
Maybe. If you are under the age of 10 then definitely yes. If your "lazy eye" has vision problems or you wish to have the eye corrected it would be a good idea to get a consultation from an ophthalmologist.