You can use the consoles of your allied faction (and fly the ships if you want, the consoles work on warbirds). It's unclear how this applies to lockbox consoles but it one would assume you'll get the console of the faction you're not allied with. You're locked out of tier 5 allied ships, but those consoles are restricted anyway. It does mean you can't get a 180 degree torpedo launcher if you're F-R and own the Regent.
Romulan consoles look like they won't be in lockboxes, since all of the ones discussed in the dev blog are limited to Warbirds, and most of them apply to the singularity core, which nobody else can use anyway.
When a Romulan sides with say, the federation. They then have access to ships and their console up to T4.
same goes for the KDF.
I very much doubt that Romulan consoles will be made available to the Fed/KDF, but it could happen.
I'd imagine consoles that affect singularity cores will remain Rom exclusive. T5 consoles will remain Rom exclusive. And other consoles may well wind up in lockboxes similar to how Fed and KDF consoles wound up in lockboxes.