It is definitely possible to develop twitching of muscles, in any part of the body including around the lips and mouth. Sometimes the twitch or tremor can be so subtle that it is hard to see but can definitely be felt by the person that it experiencing it.
Most of the time, these tremors or twitching are isolated, and they are often related to muscle strain
or fatigue. For example, if you notice that the twitching tends to develop later in the day or after you have been sleep-deprived for what ever reason, then this is probably what is going on. In these cases, which represent by far the largest percentage of muscle twitches, the treatment is working on reducing stress and fatigue, getting plenty of sleep, etc. If you find that the twitching goes away completely when you are well rested, then there is probably not any reason to be too worried.
You should see your primary care doctor
about this issue. He or she can make sure there is no evidence of weakness or twitching that is more generalized throughout the body, which might be a sign of a more significant medical problem requiring additional workup.