Post-LASIK infections are extremely rare, and Acanthamoeba keratitis is quite rare too. It is theoretically possible, but I have never come across such a case (of post-LASIK Acanthamoeba keratitis). Having something like this happen could possibly point to a breakdown of sterilisation measures.
Classically, Acanthamoeba keratitis is associated with contact lens wear, especially when the contact lens wearer uses tap water or homemade saline to wash/rinse their lenses.
If a post-LASIK patient does develop Acanthamoeba keratitis, the treatment is quite similar to someone who has not had LASIK before.
This would involve very intensive, hourly, administration of eye drops such as Chlorhexidine 0.02%, and Desomedine. Chlorhexidine is quite irritating and must be used in a particular concentration under close supervision, otherwise significant side effects can occur.
Depending on the situation, other measures may be necessary, including surgical procedures, to firstly clear the infection and secondly to provide as good a visual outcome as possible.