Is there a way to install two or more instances of LRTimelapse? I would like to be able to work with two LRTimelapses on the same computer at the same time.

No, this is not officially supported and also wouldn't work well. Also you wouldn't speed up anything.
If you have a LRTimelapse license, it will use all of your processor cores in parallel and max out the usage of the computing power provided.
If you are on the free version and have a computer with more than 4 cores, you can speed up things by buying a license and increasing the number of used cores in the settings.