If you get punched in the mouth, there is a good chance that your lip will swell. Similarly, after a piercing is done in the lip or in the area surrounding the lip (such as a labret), many people will experience some degree of temporary swelling.
This swelling will subside over the first week (and often even more quickly). However, care must be taken in the selection of the jewelry to ensure that it can accommodate any such swelling. If not, the jewelry can actually sink right into the hole and become embedded. While it is true that some people experience little to no swelling, under no circumstances should jewelry in a lip piercing sit snugly when freshly pierced. It is recommended that even when healed there is some minor play in the jewelry's fit.