I tried setup eyelashes with uv texture without using shaders nor hair particle system, because hair particle system is a bit naughty and I'm going to use it later on in three.js, which doesn't welcome complex shaders. What I tried is assigning a transparent material then map the eyelashes to uv texture, but I can't get it working correctly. As you can see the eyelashes still has a bit translucent surface around. Also when I turn on 'receive transparent shadows' on face mesh, it somehow still receives a complete solid shadow. The light in scene is lamp-spot light. .
If you have a .jpg/.jpeg texture for lashes/hair, set the material's specular-intensity value & transparency alpha value to 0 to show lashes correctly in Blender. The problem of this is that it will look fine in Blender, but if you export to .gltf/.glb file, the lashes/hair will be invisible.
So the only solution I found so far is to use a normal material but with a .PNG texture that has background removed. A little Photoshop work.