Geodesic
A compactly generated lattice with unique complements is distributive
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 617-620 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is known that in a lattice with unique complements, the modularity, atomicity, de Morgan, and other conditions imply that the lattice is distributive. It is proved that a compactly generated lattice with unique complements is also Boolean. 
@article{MZM_1972_12_5_a15,
     author = {V. N. Salii},
     title = {A compactly generated lattice with unique complements is distributive},
     journal = {Matemati\v{c}eskie zametki},
     pages = {617--620},
     year = {1972},
     volume = {12},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a15/}
}
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V. N. Salii. A compactly generated lattice with unique complements is distributive. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 617-620. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a15/