Medium Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Confusion; Time Pressure
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Procedure; Aircraft
I was on the Local Position with a Cessna in the pattern and Aircraft X cleared to land RWY 22 on a visual approach.  A departing Aircraft Y pulled up the runway and reported ready for takeoff.  Aircraft X was the next aircraft cleared to land and was 3 1/2 miles from the runway when I cleared Aircraft Y for takeoff; giving him the position of Aircraft X.  This normally would have worked without any problems; however; Aircraft Y took an unexpected lengthy time to begin his takeoff roll.  To add to the issue; the arriving Aircraft X was going faster than expected.  I told Aircraft Y no delay and he seemed to still take longer than normal to begin rolling.  When Aircraft X crossed the runway threshold; Aircraft Y was airborne approximately 5;000 feet down the runway.  About 1;000 feet short of the 6;000 feet same runway separation requirement.  I did not send Aircraft X around because I felt a safer situation would result if I allowed the Aircraft X to continue his landing instead of having two aircraft departing the same direction in close proximity to one another.  Aircraft X landed with no problems and Aircraft Y was switched to Departure.I could have asked Aircraft Y's pilot if he would be able to accept and immediate take off; however that would have required even more time for his decision and response.
LEX Local Controller reports of an operational error due to lack of runway distance between an arrival and a departure.