Lollipop is not causing battery failure, batteries fail from time to time, and Lollipop is definetly not a battery problem, if it causing battery drain you need to investigate it further to see the real cause, it isn't Lollipop, it's something else...
Is it worth it to fix? I don't know, depends on how much you have to get invested into it, will you replace it yourself or have it done? If you do it yourself it is probably worth it, the battery is around $20 and a battery back door is under $10 on eBay, not bad... If you have it done it will cost anywhere from $80-$150, and you can buy refurbs for that with a warranty from
Expansys or other supplier.
This is still not touching on the fact this is a 2+ year old phone, is it worth it for that when you can get much newer devices for under $200, like the Moto G, Asus Zenphone, half-dozen Blu devices, etc??? Ultimately, this is something you have to decide for yourself...