Honestly it is probably not the actual menthol in the juice that's giving you sores. There are a few possible reasons why you're getting these sores.
1: if you just switched to vaping recently and quit smoking, it's likely that the sores are just from withdrawing from traditional cigarettes.
2: if you are vaping low quality juice such as Dekang, chances are there may be some quality issues with the actual PG base. A lot of people have "disowned" so to speak, dekang juices for this reason exactly.
3: if your menthol juice is all PG and your other juices aren't, you're probably not drinking enough water. Dehydration causes mouth/lip sores.
Hope you get this all sorted out. Good luck.