I could be wrong, but my understanding is that any distribution from the plan must meet a defined form of payment. This would be some sort of lifetime annuity or a lump sum equal to the present value of the accrued benefit (or account balance if cash balance plan). An in-service distribution just means that a participant who has attained normal retirement age (NRA) doesn't need to separated from service in order to qualify for a distribution. The distribution paid still needs to satisfy one of the optional forms of payment stated in the plan document. IOW, I don't think a DB plan can just pay some random amount requested by a participant.
If the participant attained NRA and wanted a LS distribution, the plan can pay it (assuming no restrictions apply). If the plan provisions allow that individual to earn additional benefits after the distribution, then they could be paid those as well once they have been earned. I don't really see anything wrong with taking a lump sum equal to the full accrued benefit at the beginning of a year, then another distribution later in the year if they have earned an additional accrual, but I think most documents restrict the recalculation to once a year.
I don't think the actual funding of plan is relevant, other than if it impacts benefit restrictions.