I watched A Live Stream Reaction To Disney's Investor Day (On You Tube) They were showing clips of various Disney Properties. The One that really garbed My attention was just a quick scene of Adult Simba from The Broadway show. Then after the Clip Show Bob Chapek said "All those Movies and TV Shows will be available on Disney+, Hulu, or ESPN+
I took that to mean That Lion King Broadway is coming to Disney+. However it could just mean that Disney Insider is just going to do a segment on Lion King Broadway.
If My original thought is right, I think Lion King Broadway could drop on Disney+ in 2024 for The Lion King's 30th Anniversary.