Where to capo for F Lydian
Put the capo at fret 5 and play F Lydian using C Lydian shapes. That is the easiest of the eight positions ranked below, and it is what most players reach for. Against playing F Lydian open, it drops the mean difficulty of the key's seven chords from 3.4 to 3.4 and gains 0 ringing open strings.
You want F. Capo 5 and play in C.
All eight positions, ranked
Each row transposes F Lydian down by that many frets to find the shapes your hand would actually make, then scores the best voicing of all seven chords — fewer fingers, less stretch, closer to the nut, fewer muted strings. Lower is easier. Standard tuning (E2 A2 D3 G3 B3 E4).
What you are playing
The seven chords of F Lydian are F, G, Am, Bdim, C, Dm, Em — the ones the ranking above is scored against. Their diagrams are on the F Lydian key page.