Accommodation and convergence issues can arise during the early healing stages after vision correction surgery like Lasik.
When we look at an object, the dominant eye looks directly at the object and the non-dominant eye looks at the object at an angle. The farther the distance of the object, such as infinity, the closer the two eyes are at the same angle to the object. The closer the object is brought to the patient, the greater the angle the non-dominant eye is to the object, while the dominant eye stays straight-on. Close enough and the eyes cross. Additionally, as an object is brought closer, the pupils constrict, changing the area of the cornea through which light passes into the eye and is "seen".
It is possible that you had a small amount of misalignment before Lasik that was corrected with prisms in your eyeglasses, however you would have noticed the full alignment effect with contact lenses.
Your brain may be switching dominance because, for whatever reason, it likes the image from the other eye better. A switch in dominance most certainly could present the problems you describe.
An accommodation and convergence
specialist would likely be able to shed some light on your situation. This is most likely going to be an optometrist, although ophthalmologists who specialize in strabismus
surgery would undoubtedly be able to evaluate you. I recommend that you ask your Lasik doctor to refer you to an accommodation and convergence specialist for evaluation. This may indicate if your issue is directly Lasik related, peripherally related, is likely to resolve on its own, requires a treatment plan, is permanent, or is temporary.
All issues about convergence are predicated upon both corneas being regular and fully corrected across the entire through which light travels when the pupils are fully and naturally dilated. If there is an irregularity, such as astigmatism at the periphery of the cornea, changes in pupil size could cause the same effects you report. If the effect is different in bright light compared to lower light environments, then this could be something as straight-forward as residual or induced astigmatism
My bet would be on a treatment plan of continuing to use both eyes normally and allowing the brain to learn how to best use your new vision, but only a comprehensive evaluation by the right specialist would know for sure.