Does anyone know if you can reliably run 5.56/.223 through the Lancer .300 blackout magazines? Thank you.

Lancer recommends their 300 mags for subs only so I'd say probably not the best plan. That said only one way to prove it.

https://lancer-systems.com/product/l5awm-300blk-30-magazine/
NOTE: These magazines have been specifically designed and optimized to alleviate the stacking and feeding issues commonly experienced when running 200+ grain subsonic .300BLK cartridges in standard .223/5.56 magazines. If you are shooting lightweight supersonic .300BLK ammunition (<150gr), we recommend using a standard .223/5.56 L5AWM magazine.

Runs fine for me.

Haven’t shot 5.56 or .223 out of my Lancer .300 BLK magazines, but I’ve shot plenty of supersonic .300 rounds out of them and they work fine.

Magpul just introduced a new 20rd magazine, for 300bkt, that I'm looking forward to trying out. Check'em out.
Magpul 300bkt

Same.

I only run lancers and I’ve ran plenty of supers (110gr-150gr) out of them and subs. They are all I will run in my 300BO.