I want to get into MC Speedrunning on 1.16.1, so I'm using Fabric. While I know that Sodium is allowed for speedruns, I'd like to know whether Lithium and Phosphor are allowed for 1.16.1 speedruns as well.

Please replay as soon as possible. Thanks!

They are allowed
If you go to the leaderboards - > rules - > category rules and scroll a bit you will read:
"Fabric Loader, and the CaffeineMC mods (Sodium, Lithium, and Phosphor) are allowed for 1.15+"

Okay. Thanks, @BSRFBSRF!

Lithium and Phosphor are of course allowed. But Starlight is also allowed and it's far better than Phosphor. I recommend you to install Sodium, Lithium, Starlight and LazyDFU.
Mods Link↓
https://www.minecraftspeedrunning.com/public-resources/mods