The SAM check a prime runs is mostly an exclusions search plus a read of your public entity record, and a state tax lien isn't part of either.
FAR 52.209-6 bars a prime from subcontracting above the FAR 9.405-2(b) threshold with a firm that's debarred, suspended or proposed for debarment unless there's a compelling reason, and 9.405-2 ties that to an active exclusion record in SAM. So the exclusions search is the main event. The same clause has the prime get your written disclosure on whether you or your principals are excluded, so expect that line in the teaming paperwork.
On the entity side they see status, expiration date, UEI, CAGE, NAICS codes, size and business types from your reps, and the responsibility information, which is where a termination for default or an administrative agreement would show. A careful prime also confirms the SDVOSB certification in SBA's own search instead of trusting the SAM reps.
A lapse that's already fixed just shows as active with a newer activation date. I've had clients worry about that exact thing and the prime never brought it up once the record was active.
The tax reps in SAM, like FAR 52.209-11, ask about delinquent federal tax liability. State liens don't live there. If a prime wants that, they run their own credit check, which is a separate conversation.