Mouthwash is helpful because it will kill any bacteria that might be irritating it.
Check the ingredients on your toothpaste. Most toothpastes contain sodium lauryl sulfate or sodium laureth sulfate, both of which don't cause canker sores but can irritate them, so try to fiind one without that to use when you have cold sores. Usually the baking soda toothpastes don't have those ingredients.
Avoid acidic foods touching your canker sore. Rinse immediately after eating.
I really don't know if the lysine helps, but it does help with cold sores.
It can't hurt to take some things to boost your immune system - vitamin C, olive leaf, echinacea.