1.16.1 has a glitch which makes lagspikes when entering some chunks and it would be much easier to do it on some other version, maybe 1.15.2
I have the same problem with lag spikes and it sadly makes it unplayable. I even have the lowest possible video quality settings enabled. Also the texture pack tortures my framerate.
Every single time that I get to about the 3rd jump on the faces cp I get a mid-air lag spike. It happens again and again even after restarting the same cp several times. This is a 1.16.1 bug. This also happens to me on manacube. This is because every time you restart, the chunk that loaded to cause a lag spike unloads due to it now once again being slightly out of render distance. And changing render distance just changes the position of the lag spike. So in other words, this is unplayable for me. Also, my fps with the texture pack starts at about 5 and works its way up to 10...
Just this map, which has the lag spikes before the resource pack, and then has constant lag after. Other maps and servers run just fine for me.