That is possible in a stout press with a really good lube like Imperial Sizing Die Wax, but in my experience it's better to turn down the base and rim slightly. This doesn't require a lathe, just putting the case over .308 diameter rod in a drill motor, and using a fine file while the case is turning. As I recall, using the decapping rod from any .30 caliber Lee Loader as the rod is how I did it.
It's also possible to reform .220 Swift brass to work in the .303 Savage, without any "turning."
Did both when .303 Savage brass was scarce, but it takes a while! As I noted in Chapter 42 of the first Big Book of Gun Gack, "Loading the Savage Rifle Rounds," it took me about 20 minutes to make .30-40s into serviceable .303s. .220 Swift brass is easier (if you can find any), since it only needs to be necked up, trimmed and sized.
