I would get a second opinion from a very experienced Lasik surgeon, and by the way, not some Lasik chain store. Bargain discounts are not what you want here. As you hear so often, every individual is different, but I don't necessarily see a history of strabismus as being a major contradiction to lasik. I would be cautious if you have amblyopia or one lazy eye that cannot be corrected to normal vision. In that situation, you might only have one strong healthy eye and would want to choose your options even more carefully. People with amblyopia sometimes think that lasik can correct it but it can only (in best care scenario) give you the vision you would get with glasses.
MJK MD