So your delimma is whether you should make a starter for your lager, or brew a whole batch of beer, ferment it with lager yeast at ale temps, then rack your lager on top of the yeast cake?
Just make a starter for your lager yeast, and be done with it.
May you go marching in three-measure time
Dressed up as asses, drunk to the nines
Swing from the rafters, shouting those songs
Gone unsung for far too long