Welcome back to reloading and to TFL. We could spend days just talking about each question you have. There are a lot of posts out there on each of these topics, if you use the search function at the top of the page you will find tons of information that you are seeking.
You are asking about two different rifles that will require different case preperation (unless you are just plinking) for match requirements.
In terms of accuracy, where does lake city 5.56 brass stand when compared to Lapua, nosler, winchester, hornady, and federal? Would it just be better to use 223 brass in the 5.56?
I have yet to find a set of 5.56 dies to resize my brass, so anything you will be making will be .223 sized cases. (sad but true)
This is a personal opinion so do not get upset, but I think that any Mil-Surplus brass is junk. Heavier brass harder to resize, crimped primers that break you decaping pins, primer pockets that have to be swedged, less case capicity have to adjust powder loads, ect......
Of the cases you mentioned, Lupua would be the best but most expensive as well, I like softer brass for my 223s and personally think that the Winchester 223 cases are easy to work with and serve me well, as to the number of times they will be useful I can not say but 5 or 6 times should be without any problems. (as always check your cases after each use)
As to annealing, I do not do that since the supply of cases is plentiful and any cases that show wear are tossed. But those that do anneal, do so after the second use of the case.
As to the Hornady LNL OAL gauge use, I use the gauge and modified case in 223 along with the bullet I am using to get the MAX OAL and then back down the OA by 0.050 from that.(that is the jump my Savage likes) This is for my bolt action Savage in 223, for my ARs I load for the mag length so using the gauge is pretty useless. (unless I want to use my AR as a single shot rifle)
Hope this helps a little.