There are many conceivable ways to map 15edo onto the onto the Lumatone keyboard. However, it has 3 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. You can use the extremely flat 8\15 fifth of 640¢. This layout preserves the location of the octave, and places the down-fifth where the fifth usually is.
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This makes fingerings for most simple chords awkward though. The mappings that organise its intervals that make it easy to find consonant chords, in order of increasing compression, are the Porcupine, Blackwood, and Hanson mappings.
Blackwood avoids the contorsion problem of 15edo by dividing the octave into five sections. Dividing 15edo by 3 gets a 3L 3s scale on top of this. With a 3:2 step ratio, this also makes for easy division of the octave into three sections, as in Augmented, specifically Augene. This also functions as a Kleismic (Hanson/Keemun/Superkleismic) 4L 3s (3:1 step ratio) mapping. The range is a bit under 6 octaves, and while octaves slope up as expected for Blackwood, they do so in a way such that the vertical repeated notes cause double octaves to be nearly level.
3L 3s (right, down-right) and 4L 3s (right, up)
This version is optimized for playing the 3L 3s scale; it makes the 4L 3s scale slope upwards, although with care it is possible to use the vertically repeated notes to avoid a vertical wraparound.
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3L 3s (right, up) and 4L 3s (right, down-right)
This version is optimized for playing the 4L 3s scale; it makes the 3L 3s scale slope upwards, although with care it is possible to use the vertically repeated notes to avoid a vertical wraparound. Bryan Deister has demonstrated this version in Waltz in 15edo (2025).
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Hanson
If Hanson is most of what is needed and Augmented and Blackwood are not a priority, it is possible to compress the layout to a 4L 1s scale (4:3 step ratio) and increase the range to over eight octaves that are nearly level.
