You're not deployable for 6 mo after the surgery, so you'd probably have to pursue it on a non-operational tour (school or shore duty). The other time you might be able to do it is if you are assigned to a ship in overhaul, since that ship isn't going out to sea for quite some time.
Initial ascession schools are usually not very forgiving for taking time off to get things like elective surgery, but that will be between you and the CO of supply school. Even with LASIK, you're probably looking at missing a day or two of classes to recover. Most docs I asked did the surgery on Mondays, with very few doing it on Thursdays.
You can do one of two things: you can pursue it through an MTF or through a private civilian doctor. To do the latter, you simply need your COs permission and the money to pay an opthalmologist. The civilian opthalmologist does the surgery and all follow-up care through recovery, which is typically 3-6 months. Note: If there are any complications that disqualify you from service, it will be a 'not in the line of duty' and you will be administratively separated. Basically, that means the military says "so long" and you find yourself suddenly unemployed.
To do the former, you have to get an eval done by the surgeon's optometrist, fill out a 1/2" stack of paperwork, and then get scheduled for the surgery. Depending on the workload of the clinic, this can take anywhere from 1-6 months for a low-priority candidate. Also, you may have to travel long distances to make these appointments and initial follow-up appointments, so that realistically means taking a couple of weeks off and staying in a hotel while you go to your follow-ups. If everything checks after a week or so, the MTF optometrist takes over your follow-up care. If they screw up the surgery to the point where you are no longer qualified for service, it's a 'line of duty' discharge so you are eligible for benefits through the VA.