If a plan participant finances her Lasix eye surgery, is her expense only reimbursable during the plan year the procedure is performed or can she submit each payment for reimbursement as she pays them? This would mean that she would be submitting for reimbursement over several plan years.

It is when the service is rendered that determines the date of service and what plan year it may be claimed within, not when it is formally billed, charged or paid.

I believe the expense must be incurred AND paid for in order to qualify for reimbursement through the flex plan....or only the amount actually paid while the participant was covered.

Prop. Treas. Reg 1.125-1, Q/A-17, "Third, the medical expenses that are reimbursed under an accident or health plan must have been incurred during the period for which the participant is actually covered by the accident or health plan in order for the reimbursements to be excluded from gross income under section 105(B). For purposes of this rule, expenses are treated as having been incurred when the participant is provided with the medical care that gives rise to the medical expense, and not when the participant is formally billed, charged for, or pays for the medical care...."
There is no regulatory requirement for a participant to pay an expense prior to be reimbursed. The date of service is when the treatement is provided and if the applicable insurance is going to pay a portion is has done so. Since Lasik is not on-going treatment, such as orthodontia, the date of service is the date the procedure is performed and the expense is for only the plan year in which it occurrs.