Lip-o-suction is a type of kiss in which the guy kisses the upper lip while the girl kisses his lower lip. Then they reverse. It's very popular with young people who like variety and playfulness in kissing. The kiss appears in numerous movies (for example, The Notebook (2004) directed by Nick Cassavetes). Here's an example of lip-o-suction 
from the movie Meet Joe Black starring Claire Forlani and Brad Pitt. Notice that she's kissing his upper lip while he kisses her lower lip. The lip-o-suction in this kiss is done very gently with a very light technique. You can see that the Brad Pitt character is using a feather-light action as he goes for his partner's lower lip. But the kiss can certainly be done with more intensity if you wish. The good thing is that lip-o-suction is perfectly safe. There's no tongue involved, so you can breathe through the entire kiss. Also, your partner doesn't need to know anything about lip-o-suction for you to do this kiss. You simply kiss the upper lip, then the lower lip. If your partner wants to follow your lead and imitate you, that's fine but it's certainly not necessary. In other words, lip-o-suction can be done by one person to the other without having the kiss done back.
How to do lip-o-suction?
Doing lip-o-suction involves kissing just one lip of your partner at a time. Begin on their upper lip, then kiss their lower lip.