A B757 FLT CREW ON APCH; EXPERIENCED A FAILURE OF THE L HYD SYSTEM. EVEN THOUGH BRAKES WEREN'T REFERENCED IN THE PROC; THEY FOUND ON LNDG BRAKES WERE INOP; SO THEY EXECUTED A GO-AROUND AND LANDED WITH RESERVE BRAKES.

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ON APPROACH TO ZZZZ; WITH ACFT CONFIGURED WITH GEAR DOWN AND FLAPS 20; GOT L HYD QTY (CREW AWARENESS) AND L HYD SYS PRESS EICAS MESSAGES AS FLAP HANDLE WAS BEING MOVED TO FLAPS 30. GOT TE FLAP DISAGREE MESSAGE; RETURNED FLAP HANDLE TO 20 POSITION. HEARD A NON-NORMAL GRINDING AND SQUEALING SOUND. RAN HYD SYS PRESS CHKLIST (L ONLY) AND TRAILING EDGE FLAP DISAGREE CHECKLIST. TE FLAP DISAGREE MESSSAGE EXTINGUISHED. LANDED WITH FLAPS 20 AND REF 20. UPON TOUCHDOWN; APPLIED BRAKES AND GOT NO RESPONSE FROM THE BRAKE SYSTEM. PERFORMED A GO-AROUND AND LEFT GEAR DOWN. RWY WAS WET WITH STANDING WATER; WE SUSPECTED HYDROPLANING. RAN L HYD SYS PRESS CHKLIST AGAIN LOOKING FOR REFERENCES TO BRAKES. FOUND NO REFERENCE TO BRAKES; R HYD SYS PRESS WAS NORMAL. ACCUMULATOR PRESSURE WAS NORMAL. WE ALSO CHECKED THE FUNCTION OF THE BRAKE SOURCE LIGHT; WHICH CHECKED OK. GOT POWER TRANSFER UNIT FAIL STATUS MESSAGE. WE DECLARED AN EMER AND ASKED FOR THE EMER GEAR. MADE SECOND LNDG ATTEMPT; FLAPS 20; REF 20. NO BRAKES AGAIN. BOTH PLTS VERIFIED ZERO BRAKING; PERFORMED SECOND GO-AROUND. ACARS'D COMPANY; ASSESSED DIVERT OPTIONS; AND RAN RESERVE BRAKES CHECKLIST. DUE TO FUEL LIMITATIONS; ELECTED TO MAKE A THIRD ATTEMPT AT STOPPING THE ACFT; THIS TIME WITH THE RESERVE BRAKES SWITCH DEPRESSED. SUCCESSFULLY STOPPED ACFT ON RWY USING RIGHT REVERSER AND RESERVE BRAKE SYSTEM. SHUT DOWN ON RWY AND GOT TOWED TO RAMP.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES NO FOLLOW UP YET FROM THE COMPANY ON HOW THE BRAKES COULD HAVE BEEN AFFECTED BY THIS L HYD SYS FAILURE. EXAMINATION OF HYD SYS SCHEMATIC APPEARS TO SHOW A COMMON LINE THAT BETWEEN L HYD SYS AND BRAKE HYD SYS THAT MAY ACCOUNT FOR THE BRAKE FAILURE. HE FEELS IT WOULD BE A GOOD IDEA TO HAVE A NOTE IN THE PROC ALERTING CREWS TO THE POSSIBILITY OF ABNORMAL BRAKING SO THEY WOULD NOT BE CAUGHT UNAWARE.