Factor the number 36. You only have a few options.
- 6, 3, 2
- 4, 3, 3
- 4, 9, 1
- 2, 9, 2
- 36, 1, 1
- 12, 3, 1
I think that's all of them. Assuming logic, then #6 is most likely to be out as that's a huge difference in ages, and we have no information on a second marriage. To assure all of the children are in school and they are there for so long, we should also discard any sets with a 1 in them. That leaves 1, 3, and 5.
We have no information on twins, so we can't discard 3 and 5 just yet. However, it's highly unlikely a two year old child would be in school. So we are left with #3 as the children's ages. Hence Lily (probably) is the eldest, which also dovetails with the long hair remark, which I think is a kind of red herring.
No idea why he's lying, except for the likelihood of children that young not being in school so late in the day.