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.
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 2sQuadrasruta 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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Biyatismic (Zeus)
Bryan Deister has used a Biyatismic (Zeus) layout with a 7L 1s scale (9:5 step ratio) for 68edo, as demonstrated in microtonal improvisation in 68edo (2025). The rightward generator 9\68 is a combination of the Alpharabian tendoneutral second ~12/11 and the undecimal submajor second ~11/10, and two of these make a near-just classic minor third ~6/5, with the biyatisma (121/120) being tempered out. The chroma of the scale (4\68, upwards on this layout) is the near-just diptolemaic chromatic semitone ~25/24, and is convenient to use as a second generator (even though such is not required to avoid contorsion) to access other consonant intervals quickly, although sometimes with strange preferences built in — for instance, the septimal whole tone ~8/7 is much easier to reach (at 13\68) than the Pythagorean whole tone ~9/8 (which requires a substantial vertical reach at 12\68), while the septimal minor third ~7/6 (at 15\18) is a much longer vertical reach than the classic minor third ~6/5 (at 18\68), and the septimal major third ~9/7 is a much longer vertical reach (at 25\68) than the classic major third ~5/4 (at 22\68). Fortunately the fourth (~4/3, at 28\68), the Axirabian paramajor fourth (~11/8, at 31\68), the Axirabian paraminor fifth (~16/11, at 37\68) and fifth (~3/2, at 40\68) are all easy to reach as long as they do not go through a vertical wraparound (as happens to the fourth in the bass octave). The range is four octaves plus two notes, and octaves slope upwards — not severely, but a vertical wraparound is unavoidable if note 0 is placed to get complete octaves as defined to reach from note 0 to note 0.
