I did ferment a pilsner in a cool brewing jacket.
Primary fermentation was no problem.
Lagering was a pain. With about 12 frozen water bottles swapped out on a daily basis I was able to easily keep 4.5 gallons around 42*. I share one freezer with 4 other people in my apartment so messing around with all those water bottles was a pain for me. If you have more space and are willing to change a bunch of bottles every day + having a few extra in the fridge for when bottles don't freeze in time, it will be doable.
I would just use a altbier yeast for primary and due a 2 week lager below 45*.