So first off, there is a good thread on facial lac repair pearls somewhere in this forum and I would suggest looking it up
Second, these are just random pointers and I welcome anyone else to chime in with additional/differing viewpoints.
So when I see a lac in the ED I first run through a mental checklist.
1. Region - forehead, cheek, chin lacs there better be a damn good reason why the ED can't repair these. These are regions with few aesthetic landmarks and basically anything you do is probably going to be fine. Versus Lip, nasal, or ear lacs where the ER may be freaking out but I know that with aligning a few key points I'll get a good result. Eyelid lacs, there better be a good reason why we aren't going to the OR.
2. Collateral damage - in the face, I want to know three things before I start sewing. Is there a facial nerve branch out? Is the parotid duct involved? Is the lacrimal system ok? I literally ask myself these three questions before suturing any facial lac because it's REALLY easy to miss an injury. Goes without saying you should document all of these exams.
3. Plan for anesthesia - you gotta know your local blocks for the face, as you can repair some gnarly lip lacs with an infra orbital or mental nerve block. Aesthetic landmarks have to be lined up before you infiltrate any local in the region of the lac, and again this is where blocks can help. In the scalp, forehead, or ear (or literally ANYWHERE) local with epi can cut down on bleeding. Sometimes I like to do a regional block for pain and then infiltrate the lac with local for hemostasis.
4. Cleaning. This is where the ER messes up ALWAYS. You have to irrigate the bejesus out of these wounds, and then do it again. At minimum, I use a liter of Bernadine/saline mix followed by a liter of saline. 3 liters is probably safer. Retained debris leads to tattooing and infection.
5. Repair. So you have assured yourself that there is no facial nerve injury, the lac doesn't involve the eyelid, and you're 100% sure the parotid duct isn't involved. General principles - minimize buried suture and align anatomical landmarks. For a cheek lac this may mean just putting a bunch of interrupted 5-0 or 6-0 prolene. For the lip, you want to put the mucosa together with something quick absorbing : 4-0 chromic or plain gut. Then the muscle with 4-0 cicely. Aligning the vermilion-cutaneous junction and wet-dry lip is something your resident should probably check, since a step off of 2mm can be noticed at conversation distance, but get that aligned before you infiltrate local for sure. For the ear, if the lac goes through the cartilage, don't go crazy with cartilage sutures - you only need them if there is displacement of cartilage and even then, just place a couple slow absorbing (4-0 or 5-0 monocryl or odd) in the cartilage to re-align. Bolstering an ear lac is the biggest thing to remember.
Don't forget that any permanent suture you place will need to be removed, and if it's a small kid or drug-addict street fighter you may want to just place absorbable sutures to avoid the need for suture removal.