Muscle is muscle whether it is on you legs or your face. They relax (which is a good thing during a long night's sleep) for most of us... The exception: Vulgano Brother, who dreams of Jennifer Aniston all night, with his lips smacking the entire time, which gives him the edge over us mortals... but I diverge:
Like any muscle stretching (like before running), getting the memory back into the lip muscle may take a bit more warm up. Buzzing on the way to school is cool. Another thing that I really like is... yep... long tones. The morning was made for long tones. This is how we start my Middle School band out at 7:50 on Tuesday and Thursday mornings, then after a few exercises, progress to slurs, then to scale studies with tonging drills added. After this, you're good to go for the day.