Seems like this commit to the julia-mode package removed the julia-latexsub function which is called by ess-julia-latexsub-completion.
julia-mode does provide its own pair of capfs for this purpose, namely julia-mode-latexsub-completion-at-point-before and julia-mode-latexsub-completion-at-point-around. Perhaps ESS could just add both of these to completion-at-point-functions for both ess-julia-mode and inferior-ess-julia-mode?