I played 3 matches of historic on my phone, the first 5 minutes or so was a decent experience, but it kept getting more and more laggy. This was especially noticeable when the turn got passed to me and my permanents were untapping but everything was slowing down to a crawl. My opponent would attack and it wouldn't move to my blockers phase for 5-7 seconds, and I know my clock was actually ticking because I'd see the rope start burning when the app stopped being frozen.

Eventually the app completely crashed and I roped out and lost the match.

Because it got worse after some time having the app open my guess is the issue is related to memory leaks?

The audio started playing a static buzzing sound as the lag got worse and worse, and finally that buzz became constant and the app was completely unresponsive. Eventually Android came up with the "Magic Arena is not Responding" pop-up on the screen.