I've always used Ballistol in my sidelocks. More because they use black powder than anything else.

In my inlines I use Remoil. The same as my CF guns. I do clean it out with alcohol before shooting. I thought I was getting it all out, but now i'm not sure.

It doesn't seem to affect my first shot too much. I've shown this target before. 100yds. First shot is the lower right shot. Next two are fouled barrel. BH 209.