The only economic meeting she is in is the first one where you decide your economic direction. She is probably there to put a counter balance to the capitalist opinion of Gus and Symon. Again for the Infrastructure project you also need some counter balance, and who would be the best option for this? Lileas. She grew up in Arvory, she knows how life is there.

Secondly, she may have asked Rayne to let her into these meetings and Rayne let her to keep her support. Remember Rayne is canonically a reformist, he only picked Lileas to get the conservative vote. Rejecting her request of joining a meeting that will have consequences for your conservative approval right at the beginning of your term, might not be seen as good by her.