Hi,
Byblis filifolia seedlings can easily be transplanted. Simply use a knife or something similar to scoop up the plant and surrounding soil. In my experience, they are rarely affected. Byblis lamellata is a different matter. I've transplanted both B lamellata and B gigantea seedlings before. You must, again get as much of the surrounding soil as possible- cut the pot if necessary. I'd plant the seedling in the middle of a six inch or larger pot full of peat:sand
erlite. The problem is that B lamellata/gigantea seedlings tend to wilt when moved. I have found that, after transplant, they need high humidity. They will then recover if they wilt. I use the top 1/4 of a large Coke bottle. I place this over the newly transplanted seedling. After a few days, I remove the screw top from the Coke bottle, and after a few weeks, I remove the Coke bottle altogether. If, after removal of either the top or the bottle, the plant wilts, simply put it back for a few days, and it should quickly recover. Another couple of points, firstly, do not throw away the old pot- some seeds may germinate later. Secondly, moving the lamellata is a risk, but is one that you must take, unless it is already in a large (6"+) pot. Thirdly, good luck- once in past seedling stage, B gigantea & lamellata are very easy to grow. All of the following plants were moved in their infancy:
B lamellata seedling, a few weeks after being transplanted.
Same plant, 10 months later
Same again.
Some shots of the closely related B gigantea: