I see. It’s very difficult for a single lens to achieve high collection efficiency without having extreme curvature and thus chromatic aberration.
To toot my own horn, here’s a calculator that estimates the collection efficiency of a lens given diameter and focal length.
They still have very long focal length relative to diameter, so a single eyepiece lens alone won’t suffice. What I ended up doing is use it in combination with another small convex lens to serve as a collector, which takes the Lambertian emission of the bare emitter and turns it all into a narrow cone to feed into the main optic ( a large Fresnel lens) with a long focal length. This also enlarges the apparent size of the emitting surface, which improves imaging quality.