Let $A=\{n_1<n_2<\cdots \}\subset \mathbb{N}$ be a lacunary sequence (so there exists some $ϵ>0$ with $n_{k+1}\ge (1+ϵ)n_k$ for all $k$). Is it true that there must exist a finite colouring of $\mathbb{N}$ with no monochromatic solutions to $a-b\in A$?