I'm inclined to agree with HaleElven.
Once you have maxed out an LI, you can't upgrade it any more. You can fine tune them a bit but that can take a while and your character will be levelling up the whole time. By the time you get an LI to it's maximum potential, your character will have out levelled it while you are still levelling up. Once you reach the level cap, that's when you can put the time and effort into getting the most out of an LI, because you'll be at the highest level the game offers and can't out-level an LI any more (until the level cap goes up again).
You'll pick up third age LI's as loot from mobs, or you can buy them from the auction house, or craft them if your crafting skill is high enough (and you have the right craft to make the type of LI you want). Relic Masters can "meld" third age LI's, but only for certain character levels. You can also barter skirmish tokens at any skirmish camp for 2nd and 1st age symbols to craft 2nd and 1st age LI's (there are no level 95 1st age symbols or LI's in the game yet), plus the epic quest chain will give you a 2nd age symbol as a reward in a couple of different zones. You also have a small chance of getting a 2nd or 1st age symbol from hobbit presents or dropped loot boxes.
Right now, a level 95 2nd age LI is the best the game has. You get a lvl 95 2nd age symbol you can craft an LI with when you complete the epic quests for Helm's Deep, there's a reputation vendor inside the Helm's Deep fortress that will trade more lvl 95 2nd age symbols for tokens you can earn in western Rohan, plus skirmish camp vendors offer them for skirmish marks/medallions.
Therina - Hobbit Guard Rongo - Hobbit Warden
Frood - Man Minstrel Garmun - Man Captain
Zorosi - Dwarf Champ Froodaroon - Elf Hunter
Southern Defenders - Arkenstone (formerly Elendilmir)