Why would they need a base? Freespace fighters have magical reactor producing endless amounts of pixiedust for both the ships power needs and subsystem repairs. And the pilot can live on recycled pudding for weeks if need be. Only thing they would need a base for is hull repairs and munitions resupply. Except if the pilots are very careful...
We saw, was it two, destroyers accompanying the Lucifer. Maybe one or two more we didn't see. A destroyer weren't in system, but sortied a fighter escort for Taranis from some other system. Shivan fighters do seem to have some uber jumpdrives afterall, judging from the many mission they have been seen using a node. Both FS1 and FS2. A Shivan destroyer doesn't even have to be in the contested system. It can provide fighter and bomber support trough nodelines.