In FRLG, all the berries you can find without Pick-Up are from those little dark patches on the ground. In the Berry Forest, in the northeast corner of that area at the end where you find Lostelle, there's another of these patches. In that patch is a Lum Berry.
As Dunsparce said, however, it's not always there. Just walk around a lot, return and see if it's there. If it isn't, repeat. If it is, woohoo, you have a Lum Berry.