Is it possible for someone with a lpd to get pregnant and deliver at full term?

Definitely: If you have a confirmed luteal phase defect, then your big risk is for recurrent miscarriages, and so once you conceive you should be treated with supplemental Progesterone through the first 10-12 weeks of pregnancy (different dr's, use different durations), but as long as you have sufficient Progesterone support in the 1st trimester, beyond that no increased risk for preterm delivery (based on hx.