Is eye surgery for a lazy eye a good option to consider?

Depends. Depends on if correcting ambylopia, strabismus, or both. If eliminating the cause such as a congenital cataract, then yes. If the eyes are very misaligned then extraocular muscle surgery will help.
Only if necessary. Eye surgery for amblyopia is generally considered for congential cataracts and true strabismus. Often, glasses or contact lenses may be tried first with patching and/or Atropine drops as first-line treatments.