ProPresenter and ProVideoPlayer can be run simultaneously from the same Mac, but this is not recommended or supported. You will need to be proficient at assigning your outputs correctly in both programs in order for this to work. You could also use Text Stream from PVP2 to get your lyrics from ProPresenter into PVP on the same computer. This would free up all of your outputs for PVP if you only need lyrics over your media.
If you are using PVP3, this would need to be handled through an NDI output over your network from ProPresenter.
We do not have a recommended way of setting this up since this is not a supported setup. We will always recommend two computers when running both programs simultaneously.
If you just need to have both programs installed on the same computer and you use them individually, then there won't be any issues at all with that.