B767-300 CREW LOST ALL OIL QTY AND THEN HAD LOW OIL PRESSURE.

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JUST S OF CINCINNATI; OH; IN CRUISE AT FL330; IN MY SCAN I NOTICED L ENG OIL QTY AT ZERO WITHOUT ANY EICAS MESSAGES OR WARNING LIGHTS DISPLAYED. L ENG OIL PRESSURE WAS OBSERVED LOW BUT WITHIN OPERATING LIMITS. WE DSNDED TO FL260 AS A PRECAUTION AND REVIEWED THE FLT MANUAL FOR ANY APPROPRIATE IRREGULAR PROCS. DISPATCH AND MAINT CTLR WERE CONSULTED AND IT WAS AGREED TO CONTINUE TO ORD. OIL PRESSURE CONTINUED TO SLOWLY DETERIORATE AND APPROX 40 NM SE OF ORD PRESSURE DECREASED BELOW THE REDLINE LIMIT. SO; L ENG WAS SHUT DOWN IN ACCORDANCE WITH THE (L/R) ENG OIL PRESSURE IRREGULAR PROC. WE DECLARED AN EMER AND REQUESTED EQUIP TO STANDBY AT ORD. WE LANDED WITHOUT INCIDENT AND TAXIED TO THE RAMP. VERY GOOD ASSISTANCE FROM THE FO WHO FLEW THE ACFT AS WELL. SUPPLEMENTAL INFO FROM ACN 579108: AT CRUISE; CAPT NOTED ZERO OIL QTY ON L ENG. OIL PRESSURE DROPPED OFF; BUT BECAME STEADY BTWN 95 AND 105 PSI. DURING INITIAL DSCNT LOW OIL PRESSURE LIGHT FLICKERED SEVERAL TIMES; BUT PRESSURE REMAINED IN LIMITS. CONFERRED WITH MAINT CTLR/DISPATCH AND DETERMINED THAT WE WOULD MONITOR THAT ENG. AS LONG AS IT REMAINED WITHIN LIMITS; WE'D CONTINUE TOWARDS ORD. INFORMED ATC OF SIT AND REQUESTED STRAIGHT IN RWY 32L. DURING FURTHER DSCNT; PRESSURE DECLINED SLOWLY AND OIL INDICATOR ON EICAS BEGAN TO FLICKER TO RED. OIL PRESSURE AROUND 76-85 PSI. ABOUT 50 MI SE ORD; EICAS RED OIL PRESSURE INDICATION ON STEADY. ACCOMPLISHED INFLT ENG SHUTDOWN PROC AND DECLARED EMER TO ORD APCH. DETERMINED THAT ORD WAS NEAREST SUITABLE ARPT AND LANDED RWY 32L WITHOUT FURTHER INCIDENT.