B757 FLT CREW REPORTS L HYD SYS PRESS CAUTION MESSAGE SHORTLY AFTER LANDING; FOLLOWED BY NOSEWHEEL STEERING FAILURE. ACFT IS STOPPED ON TXWY AND TOWED TO GATE.

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CAPT'S LEG. TKOF FROM ZZZ WAS NORMAL WITH ONLY WHAT APPEARED TO BE A SLIGHT NOSEWHEEL SHIMMY AT ROTATION. AFTER CHKING IN WITH ZZZ CTR THEY SAID THAT THERE WAS SOME DEBRIS ON THEIR RWY AND ASKED IF IT WAS OURS. SINCE WE DIDN'T NOTE ANY PROBS OR RPTS FROM THE CABIN; AND THERE WERE NUMEROUS OTHER ACFT TAKING OFF AND LNDG AT THAT TIME; WE CONTINUED ON TO ZZZ1. APCH; LNDG; AND ROLLOUT WERE NORMAL FROM ALL COCKPIT INDICATIONS. TWR CLRED US TO CROSS RWY WHEN; AS XING WE GOT A 'L HYD SYS PRESS' CAUTION MESSAGE. AS I SLOWED DOWN ON TXWY BTWN THE RWYS I LOST NOSEWHEEL STEERING AND HAD OTHER SECONDARY INDICATIONS. I STOPPED THE ACFT AND SET THE PARKING BRAKE. WE RAN THE QRH CHKLIST FOR THAT MESSAGE. SINCE WE HAD NO STEERING; I DECIDED TO START THE APU AND SHUT DOWN THE ENGS AFTER TALKING TO MAINT. TWR AND OUR DISPATCHER WERE ALSO NOTIFIED AND THE CREW AND PAX WERE INFORMED. TUG TOWED TO GATE X. WE MET WITH MAINT CREW AFTER CHOCKING IN. THERE APPEARED TO BE A TREAD SEPARATION ON THE #7 MAIN MOUNT (R INBOARD). THE TIRE WAS STILL HOLDING PRESSURE BUT MUCH OF THE TREAD WAS GONE. AT THE GATE I TALKED WITH OUR FLT ATTENDANTS AND ASKED IF THEY NOTICED ANYTHING. THEY SAID THEY NOTICED A VIBRATION ON TKOF; BUT THEY DID NOT CALL US. I ALSO NOTED THAT YOU COULD NOT EASILY SEE THE #7 WHEEL FROM THE CABIN. I TALKED TO DISPATCH AND THE CHIEF PLT'S OFFICE BEFORE DEPARTING ON MY NEXT LEG. SUPPLEMENTAL INFO FROM ACN 756923: THIS WAS OUR SECOND LEG OF THE DAY AS WE HAD FLOWN DOWN FROM ZZZ1. THIS WAS THE CAPT'S LEG AND I ACCOMPLISHED THE WALKAROUND. THERE WERE NO PROBS NOTED ON THE OUTSIDE OF THE ACFT AND ALL THE TIRES APPEARED NORMAL DURING THIS VISUAL INSPECTION; AS THEY HAD IN ZZZ1; AS I HAD ALSO ACCOMPLISHED THAT WALKAROUND. THE TKOF FROM ZZZ WAS NORMAL WITH THE ONLY ITEM OF NOTE BEING A SLIGHT NOSEWHEEL SHIMMY. DURING THE CLB WHEN WE WERE SWITCHED TO ZZZ CTR THEY INFORMED US THERE WAS SOME DEBRIS FOUND ON THE RWY IN ZZZ AND WONDERED IF IT HAD COME FROM US. SINCE WE HAD NOTED NOTHING UNUSUAL DURING THE TKOF AND HAD OBSERVED SEVERAL OTHER DEP/ARR ACFT; WE PROCEEDED TO ZZZ1.