Yes, as SupersonicSupply says, measure the case portion to ensure it is slightly shorter than the max case length for .308. Even a "borderline" case length can make chambering and extraction "sticky".
More likely, though, the problem is as other have said; the brass was fired in a different rifle already and is stretched to that chamber, which makes it too tight in your chamber. The Lee Loader only sizes the neck. In order to get that brass to not be so tight in your chamber, you'll need to do a "full resize" which will require a press and dies for .308.
Not worth it, in my opinion. As long as the case lengths are not too long, and you can chamber the rounds, go ahead and shoot them and they might just form to the chamber better.
As mentioned, a better option is to buy unfired (new) brass or buy factory rounds and fire them (in that specific rifle) and save that brass. If you do that, and make sure to check lengths and trim if necessary, your Lee Loader will work perfectly and your brass will last a very long time.