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We prove that there exist Delone sets in $\mathbb{R}^d$, $d \geq 2$, whichcannot be mapped onto the standard lattice $\mathbb{Z}^d$ by Lipschitzco-uniformly continuous bijections satisfying an asymptotic control on thelower distortion. The impossibility of the unrectifiability crucially usesideas of Lipschitz regular maps recently introduced by M. Dymond, V. Kalu\v{z}aand E. Kopeck\'a.

Delone sets that are not rectifiable under Lipschitz co-uniformly continuous bijections