The indication listed (all three Lamps on), sounds like it may be an Open Neutral issue, on 1/2 of a Multiwire Circuit; and there is a connected Load bridging the two halves of the Multiwire Circuit. (???)
Maybe the odd report is due to a N-G bond, with some other Circuitry issue involved upstream, downstream (or both) from the Outlet tested???
In any case, suggest to remove the N-G Bond on all Receptacles, then place a GFCI Receptacle at the "First Outlet" of each Receptacle Circuit - with the remaining Outlets fed via the "LOAD" output of the GFCI Receptacle.
A GFCI Receptacle may be used at all locations, if wanted.
Without the GFCI protection, replace all Receptacles on the mentioned Loops with Two-Wire, Non Grounding type Receptacles.
As others have mentioned, back up the Receptacle Tester's test with a test using a Volt Meter.
I prefer to use a "Wiggy" (Low Input Impedance, Solenoid type Volt Meter) for a "Proof" test.
Scott
