LTT CLB THROUGH OCCUPIED ALT HAD LTSS FROM ACR. SYS ERROR.

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LTT AT FL390 REQUESTED CLB TO FL430. I ADVISED THAT UNLESS LTT COULD BE LEVEL AT FL430 IN 3 1/2 MINS; IT WOULD HAVE TO WAIT UNTIL W OF STL; DUE TO XING TFC AT FL410 (ACR). LTT RESPONDED; 'WE CAN DO THAT; WE'RE OUT OF FL390 FOR FL430 AND WE'LL BE LEVEL IN 3 1/2 MINS.' REALIZING THAT AN ACTUAL CLRNC TO CLB HAD NOT BEEN ISSUED TO LTT; THE PLT; IN MY OPINION; CLRLY UNDERSTOOD THAT HE HAD TO HAVE HIS ACFT LEVEL AT FL430 IN THE TIME PARAMETER STATED AND WHY. BASED ON THIS I ACKNOWLEDGED 'ROGER; MAINTAIN FL430.' BY OBSERVING THE MODE C ALT READOUT LTT OVER THE COURSE OF APPROX 3 MINS; I ASCERTAINED THAT THE ACFT'S RATE OF CLB APPEARED TO BE INSUFFICIENT TO MEET THE NECESSARY ALT REQUIREMENT. AT THIS TIME I TOLD LTT TO 'RPT LEVEL AT FL430 IN 1 MIN AND 15 SECONDS OR LESS; ADVISE IF UNABLE.' LTT RESPONDED; 'I'M OUT OF FL420; WE'VE PICKED UP A TEMP CHANGE.' I REITERATED; 'I SAY AGAIN; ADVISE IF UNABLE; AS QUICKLY AS POSSIBLE.' LTT ACKNOWLEDGED; 'I THINK WE CAN MAKE IT; BUT IT'S GOING TO BE CLOSE; DO YOU WANT TO GIVE ME A VECTOR?' I THEN TURNED ACR 20 DEGS L; THEREBY ACQUIRING A SMALL AMOUNT OF ADDITIONAL TIME AND SETTING UP A BETTER ANGLE FOR POSSIBLE EVASIVE ACTION. I WENT BACK TO LTT AND SAID 'I NEED YOU LEVEL IN 30 SECONDS; ARE YOU GOING TO MAKE IT?' LTT ADVISED THAT HE WAS GOING TO BE UNABLE TO COMPLY. I TURNED LTT L HDG 170 DEGS. I THEN DSNDED ACR TO FL400. LOSS OF SEPARATION OCCURRED; CLOSEST POINT WAS 1.9 NM AND 1300 FT. PREVENTION OF RECURRENCE CAN BE ACCOMPLISHED BY PLT ADVISING CTLR ASAP OF POSSIBLE INABILITY TO COMPLY WITH RESTRICTION; CTLR TAKING OTHER ACTION IMMEDIATELY UPON LEARNING OF PLT'S DOUBT.