Mats are a fact of life for Lhasas and their owners. The Lhasas get them; the owners remove them! And, unless you plan to keep your Lhasa clipped down completely, you need some pointers for removing mats.
Gentleness is the key if you intend to get rid of the mat without losing or damaging the coat and without hurting your Lhasa. Of course, if the mat isn't solidly packed, removal is easier. First lightly spray the mat with a detangler; then loosen the mat by gently pulling it apart with your fingers. I use the end tooth of a metal comb to separate the mat a few hairs at a time. Once the mat has been separated, I brush through the area to remove the dead hair and then comb through it again to make sure I have removed the entire mat.
If the mat you're removing is large and packed solid, you may have to saturate it with a mat-removing or detangling spray*. Patience is a requisite for both you and your Lhasa when you are faced with removing such a mat. Try to separate the mat with your fingers and then work on the mat from which ever side allows you the best access. Don't cut the mat out unless you want a big hole in your dog's coat and only cut through the mat as a last resort, if it is so solidly packed that you have no other choice.
To loosen the mat, you may have to use a detangling spray as you progress, and you may have to allow the spray to soak into the coat for a while before it does its job. Alternate between separating the mat with your fingers and separating it with the end tooth of your comb. Don't yank and pull because that hurts the dog, and if he gets fed up and refuses to cooperate, you've got a battle on your hands.
Of course, the best way to control mats is just not to let them happen. What a joke! Anyone who's had a Lhasa can tell you that's not possible unless you brush the dog constantly. I know someone who has such a mat phobia that she spends hours brushing her dogs each day. Her brushing technique isn't all that wonderful, and her constant brushing has done more harm than good to the coats. Her dogs aren't matted, but their coats are thin and straggly-looking. I guess what I'm saying is that "balance" is best; don't neglect your Lhasa's coat but don't brush the life out of it either.
For most of us, constant brushing is neither practical nor preferable. Brushing your Lhasa regularly (and how often "regularly" is depends on the coat stage your dog is in, the weather, the type of coat, etc.) and carefully removing mats when you find them is much more effective than ignoring your Lhasa's coat until he has to be clipped or constantly brushing until there's no coat left.
Brushing on a regular basis makes sense because it reduces the number and severity of the mats your Lhasa does get. Regular brushing reduces grooming time and allows you to spend some quiet time with your Lhasa. If trained correctly, Lhasas enjoy being groomed and are very proud of themselves when you say, "Okay, you're done! And aren't you beautiful!"