You don't seem very clear about what an EEA family permit is. If you are the EEA national (Lithuania) it is YOU who needs to be moving to the UK in order to work and live for your spouse to have the right to move.
If you go there you have to be a qualified individual by the end of the first 3 months, i.e. you must have a job/be self-employed/be a student/be self-sufficient (some of these methods have extra requirements, e.g. health insurance). What your husband does now is of no interest to the UK government at all. He has no right to move to the UK except the right that you moving with him with provide him with.
He can apply before you go there OR when you're already there exercising your EU treaty rights. It makes no difference but the documents are different. See here:
https://www.gov.uk/family-permit. A lot of the info you require can be found by a simple Google search or by viewing the other topics on this website.
Again, if you do not plan to do something in the UK (work/study/rely on your current savings) then he doesn't have the right to go there.