there are 2 eyelash asset types: under Actor, and under SkinGen 'Makeup'
The eyelash under Actor saves normally, picking from the AssetType dropdown menu during the save process.I'm assuming this is the morphs-only.

the 2nd Eyelash type saves under SkinGen 'Makeup'
I'm assuming this is the texture-only
1. Activate the SkinGen Appearance editor
2. now saving SkinGen templates is possible (Full Makeup, Eye Makeup, Eyelash…)
3. select Eyelash from the AssetType dropdown during the save process.