There are many conceivable ways to map 68edo onto the onto the Lumatone keyboard. However, it has 4 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. In addition, due to its size, it would not cover all the notes even if it was.
Diatonic
You can use the b val, but it is very flat. On the plus side, the patent 5th is directly above the flat one, so you can also use this mapping as a split-chroma relative of tetracot that requires larger vertical stretches to hit familiar chords.
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Diaschismic
The diaschismic mapping would hit harmonics with greater efficiency than the diatonic mapping, but this also has multiple unconnected rings in 68edo, requiring splitting of either the period or generator to hit all the notes. The most obvious of these would be Shrutar, but this results in either a very lopsided step size or a lot of repeated notes, making it not actually the optimal mapping for an edo of this size.
Bidia
The next option is slicing the period in 4, which produces bidia. The 4L 4s mapping covers the full gamut in the middle octaves with a minimum of repeated notes, but skips quite a few at the edges and has a strong downward slope. The 8L 4s mapping covers all the notes with a mild slope and a moderate amount of repeated notes, but with a smaller range.
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Quadrasruta
Another option is the 8L 2s Quadrasruta mapping, which gives you more than three octaves with no missed notes and only a mild upward octave slant, making all harmonics except for the 11th & 19th easy to play together.
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Antidiatonic
To give you a little more range while keeping octaves fairly near horizontal, the 2L 7s mapping generated by 31/68 works decently, especially if you favor using the 11th harmonic in compositions.
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