I just had occasion to type this and thought I'd share (fairly sure someone will have done this before, but my search-fu fails me).
ls -R | perl -ne 'if(/:$/){s/:$//;s/[^\/]*\//--/g;s/^-/\t|/;print}'
Result:
$ ls -R | perl -ne 'if(/:$/){s/:$//;s/[^\/]*\//--/g;s/^-/\t|/;print}'
|---branches
|---hooks
|---info
|---logs
|-----refs
|-------heads
|-------remotes
|---------origin
|---objects
|-----02
|-----0a
|-----10
|-----24
|-----27
|-----3f
|-----41
|-----4e
|-----64
|-----69
|-----6e
|-----70
|-----74
|-----76
|-----7b
|-----82
|-----8d
|-----94
|-----a7
|-----ac
|-----b0
|-----b7
|-----d6
|-----dd
|-----e2
|-----info
|-----pack
|---refs
|-----heads
|-----remotes
|-------origin
|-----tags
|-Spider
|---Muffet
|-----Filter
|-------Reader
|-----Output
|-------Writer