I want to discuss supporters and how they gain exerience. While my question does have implication for Lili and Haruhime, it is still a broad inquiry about supporters in general.Â
Now from previous discusions I have noted that supporters are considered to be in parties to litterally, pick up the leftovers, with little to no chance of gaining the experience necessary to advance. But, how does this explain the larger Familia's, that start their adventurer's off as supporters, so they CAN gain experience in the dungeon? I am thinking of mainly Ais, of the Loki familia, but it is not only her. She starts out as a 7 year old supporter but by the time she is 8 years old has gained enough experience to become 2nd level. Now this would indicate that they can, and do, gain enough experience to advance in level. While it does suggest that Ais was special to some degree, certainly in the speed in which she gained her level, but it also suggests that any supporter can gain the necessary experience to advance.
From this perspective, it is not unreasonable to expect Lili and Haruhme to grow within their level, even if it is less likely, though not impossible, to level up.