What you really need are measurements to avoid expensive guesswork. Then any of the great neck makers can cut it to your specifications (like Warmoth, USA Custom Guitars, MusiKraft, Guitar Mill, etc.) Sometimes it's as simple as saying I want a jazz neck that's .030" oversize. This can usually be done at little to no charge. Check out the Musikraft website as they list 4 or 5 different neck profiles and their measurements.
Or, if you have a bass with a neck that you love, you can order an oversized neck and have your favorite local luthier shape it to the same dimensions.
In terms of specs & measurements, here's a list of things you should know if you plan on ordering a custom neck (there are other cosmetic considerations but these represent the technical details):
- The thickness at several points along the neck (most importantly at the 1st and 12th frets).
- The basic shape/profile (C-shape, V-shape, U-shape, asymmetrical, etc.) or at least the basic vibe you want (Jazz shape, Precision shape, MM shape, etc.).
- The width of the neck at the nut (Jazz basses are typically 1.5" and P basses range from 1.5" to 1.75").
- The width of the heel
- The number of frets (it's very important you match the number of frets to your existing neck)
- Truss rod adjustment location (at the heel vs the headstock)
- Fingerboard radius (vintage spec is 7.25" but many players prefer something flatter, anywhere from 9.5" to 16")
- Fret wire size
- Tuner hole size
Or, you could (gasp) sell the Lull and look for something that will suit your hands better.
custom 4 string neck sourcing 
I'd sell and get something that you try before you buy...the hit you take on the Lull will probably be about the same as getting a new neck of the same quality as the Lull so why not just get a new bass that works for you.
