It'll be fine.
If forming and/or fire-forming to another cartridge, then it's worth putting more consideration into the starting point. ...For which Winchester a decent choice - especially if annealed.
But for use in a .223 Rem chamber, it doesn't really matter. Stick with the Lake City, if you want. It's plenty good. If you think it can be better, uniform them and sort by weight, case capacity, etc.
My "precision" applications of .223/5.56 brass use more LC brass than anything else, with Hornady a distant second.
(I've chased my tail a bit this year with .17-223, and learned still more about .223 / 5.56 brass and head stamps that I thought I would ever need to know. [Similar, but shorter and simpler story with 6x45mm a few years ago.] Winchester, whether 'commercial' or military stamped, fire-forms really well; and is one of the best options for moving the shoulder back and/or necking down, once annealed.)