Huh. So I just discovered something that might seem non-trivial at first... sorry if people already know this.
There's specific mission generation (albiet, if only in flavour text) for factions in a Lockdown state.
You see them by going to a station owned by a faction *other than* the one in lockdown. These stations will operate normally, and the faction in lockdown offers missions specifically about the lockdown (kinda like the War missions).
E.g
Just interesting really... since most lockdowns are generated by destroying system authorities, they'll generally own the asset(s) in the system. This just happened to be a lockdown resulting from massacre missions during a war which the faction subsequently lost. Wonder if they actually do help stop Lockdown, or if it's just flavour text like with War missions.
Another flavoured mission is "Illegal Military Plans Salvage Operation", seems to pay around 200k-500k, unlike bust-state illegal antiquities salvage, which pays out about 1m credits.
EDIT: Another is "Security Planetary Scan Job"