1. Am I allowed to use Lunar client or not?
2. I play on a pretty bad computer that can’t run obs very well is there any other recording software I could use?

1. No. You can only play vanilla Minecraft (plus a few Fabric mods)
2. If you have an NVIDIA GPU, you may want to use ShadowPlay (it's built in)

I don’t have an nvidia gpu tho

use xbox game bar (pre-installed if you have windows 10 or 11)

Problem when I use the Xbox game bar it doesn’t capture live split

Use this mod instead of Live Split: https://redlime.github.io/SpeedRunIGT/ And yes, it is allowed

@Hammyburrger22 SpeedRun IGT is the recommended timer, however there is an option in the Game Bar settings to allow the background elements and stuff to show up while you capture Minecraft. Its in the Recording section (i think since i dont have an english windus 10 install), and should cause LiveSplit to show up. This is also usefull for other games, too.