Answer
This is a genuine limitation, not a configuration gap — the target overview screen's own built-in company filter is implemented client-side on that screen, and a Lobby Element's data-source condition (even with a $COMPANY$ parameter enabled) can't override or set that screen-level filter. At best, enabling the data-source condition just adds an additional, independent company filter from the Lobby's own query on top of whatever the screen's own filter is already set to — if the two don't happen to match, the screen shows no data at all rather than the Lobby's intended company being applied to the screen.