With AR pattern, yes...however to be certain one often buys a new ar bolt with the new barrel that the mfg has already checked for head spacing. it is possible but rare that an existing AR bolt will not head space correctly with the new barrel. Again, the safe thing to do is to check head space with a gauge even when swapping an AR barrel (but in reality many people skip this step). Keep in mind there is a little more to it, such as the gas tube, gas block, etc., and if you change barrel length you have to adjust these things.... My original answer was just to say that you don't need a lathe. You still need to know what you are doing though, but again, it is all online. The main thing I guess is to make sure you have the proper blocks to mount the upper receiver in a vice, because the one thing you can screw up is twisting the upper receiver and ruining it. Most other things you can just give up and take your parts to someone who knows what to do.
To check head space you use a "go gauge", "no-go gauge" and sometimes a "field gauge". Basically the bolt closes on a go gauge but will not close on the no-go. People make a no-go by putting scotch tape on the base of the go. Google those terms and it will all be clear....these gauges are basically dummy cartridges of specific lengths. This is for bottle necked cases that head space on the shoulder datum, I'm not sure how rimmed case chambers are checked.