Is $E_{LBA}$ turing-recognizable?
I just read the definitions, hence I am not an expert on LBAs, but I think that the non-emptiness problem $\overline{E_{LBA}}$ is r.e., so the emptiness problem $E_{LBA}$ can not be r.e., otherwise it would be decidable.

To see why $\overline{E_{LBA}}$ is r.e., notice that to certify that an $LBA$ has nonempty language it suffices to exhibit a word $w$ and a trace $t$ proving that $w$ is accepted by the $LBA$. So, a semidecider only has to enumerate all such pairs $(w,t)$, and (effectively) check for each pair if it proves the $LBA$'s language nonempty.