You can not compair use on a dirt bike chain to your gear train. On the dirt bike the chain is running in the dirt and will pick up everything it can. The gear train on your lath is in a semi protected environment so it should see very little amounts of dirt or swarf. I have been using bar and chain oil for the last 20 years and there is very little mess. I bet you re using WAY to much. If there is enough to sling off then it is to much. It will sling off all that it does not need.
In your use of the bar & chain oil what amount have you found to be sufficent ?? How often should it be reapplied ?? There's a better than average chance that have been using way too much as I oil the gear train and all oil points with every use of the lathe. The reasons are twofold... 1.) The lathe is in a non-climate controlled garage & I live in a high humidity area. 2.) I'm OCD about making sure it's properly lubed to both prevent wear & rust.