I know Git stores information of when files get deleted and I am able to check individual commits to see which files have been removed, but is there a command that would generate a list of every deleted file across a repository's lifespan?

git log --diff-filter=D --summary

See Find and restore a deleted file in a Git repository

If you don't want all the information about which commit they were removed in, you can just add a grep delete in there.

git log --diff-filter=D --summary | grep delete