There are many conceivable ways to map 22edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean. This is "Preset 5 — 22-ET Bosanquet" in the official Lumatone manual.
Keep in mind that, since 22edo is a superpyth temperament, 5/4 is mapped to the interval of an augmented second (e.g. a 5/4 above C is D♯). Therefore if 0 is 1/1 on this mapping, 7 represents 5/4 and you can find that by going over to 4 (C → D) and then going up to 7 (D → D♯).
Porcupine
If you want 5-limit intervals to be accessible in a more intuitive way, the 1L 6s mapping for Porcupine may be preferable.
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10
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Magic
If you want to maximise playable range, the magic mapping is the widest one that still covers the full gamut, with the two most compressed MOSes spanning between 8 and 11 octaves. Though, the resulting 3L 4s MOS has a 6:1 step ratio, making it very lopsided.
