I've done some more testing. I can reproduce similar behaviour if I'm using a Git install that includes a broken Git Credential Manager for Windows (GCMW), essentially v1.16.1 and v1.16.2.
Sourcetree can detect the broken versions of Git Credential Manager and force the use of a working copy, v1.17.1, using the following parameters with Git calls
-c credential.helper= -c credential.helper="C:/Users/mminns/AppData/Local/ATLASS~1/SOURCE~1/GIT_EX~1/GIT-CR~1.EXE"
However I suspect this override isn't being carried through to git-lfs which is then calling Git without the overrides and uses the broken Git Credential Manager which fails to authenticate.
Until the fixed version of Git Credential Manager is shipped with a new Git for Windows release which is bundled with a new Sourcetree release please use the following work around.