Lumatone mapping for 76edo
There are many conceivable ways to map 76edo onto the onto the Lumatone keyboard. However, in the patent val, it has four mutually-exclusive rings of fifths (of 19edo), so the Standard Lumatone mapping for Pythagorean is not one of them, unless the sharp 76b val is used, and even then, due to its size, this mapping does not cover all the notes.
Diatonic
Using the 8L 4s scale of Diminished temperament, Bryan Deister has tested two 8L 4s mappings for 76edo. Both give access to both fifths of 76edo, but the version with the 8:3 step ratio favors the flat fifth, while the version with the 7:5 step ratio favors the sharp fifth.
Version with 8:3 step ratio (flat fifth favored)
The version with the 8:3 step ratio is demonstrated in microtonal improvisation in 76edo (2025). Although this is technically a Diminished layout (rank-2, with the quarter-octave at 19\76), it is probably more conveniently thought of as a rank-3 temperament layout. The rightward generator 8\76 is a near-just tridecimal 2/3-tone or trienthird, ~[[14/13]; three of these make a somewhat flat ~5/4 classic major third (the cantonisma 10985/10976 is tempered out); four of them (32\56) make the sharp (patent) version of the fourth ~4/3 (corresponding to the flat patent fifth ~3/2); seven of them (56\76) make a near-just classic major sixth ~5/3. Of the two single-key-step generators other than rightward, the upward generator 5\76 has a more convenient mapping than down-rightward (3\76); 5\76 is a slightly sharp greater vicesimotertial semitone ~[[23/22]; four of them make a near-just classic minor third ~[[6/5]. Eight rightward generators minus four upward generators reach the flat version of the fifth at 44\76 (the corresponding sharp fourth being reached with rightward generators alone, as noted above); five rightward generators plus one upward generator reach the sharp fifth, and two rightward generators plus three upward generators reach the corresponding flat fourth. The range is a bit under 3 octaves, and the octaves slope down mildly.
Version with 7:5 step ratio (sharp fifth favored)
Bryan Deister has also tested the version that has a 7:5 step ratio, but no demonstration video is available at this time. As with the 8:3 step ratio version, this is probably more conveniently thought of as a rank-3 temperament layout than a Diminished temperament layout. The rightward generator 7\76 is a flat septimal major semitone ~15/14; it also functions as a near-just classic diatonic semitone ~16/15, but only if the sharp fifth (76b val) is used (which tempers out the marvel comma 225/224); five of these make a near-just undecimal major fourth ~11/8; eight of them make a near-just classic major sixth ~5/3. Of the two single-key-step generators other than rightward, the down-right generator 5\76 has the attraction (for anyone trying out both versions of the 8L 4s mapping) of being the same as the upward generator for the 8:3 step ratio mapping; further, when used with the 7:5 step ratio mapping, its alignment with the small step scale provides added convenience, since one does not have to count chromas separately from small steps. Five (large) steps right plus two (small) steps down-right yields the sharp version of the fifth (45\76); three (large) steps right plus two (small) steps down-right yields the corresponding flat version of the fourth, putting it in the same row as the sharp fifth and the classic major third, which is one (large) step left of the flat fourth. Seven (large) steps right minus one (small) step down-right (thus plus one step up-left) yields the flat version of the fifth (44\76), while six (large) steps right minus two (small) steps down-right (thus plus two steps up-left) yields the corresponding sharp version of the fourth (32\76). The range is a bit under 3 octaves, and the octaves slope down mildly.