After a NGT LNDG on north side of Los Angeles Intl Arpt, Cessna 310, N98834, was taxied south (S) to Delta cargo area. Bfr rchg S rwys (25L & 25R), the plt stopped short of Kilo ramp bhnd another Acft (N61C) & contacted S Gnd Ctler (GC-1). He was told to hold short. Cont Flt 866 (Boeing 727, N88704) adzd S Lcl Ctler (LC-1) he was ready for tkof (on Rwy 25R). LC-1 was aware N98823 & N61C were waiting to cross S rwys & granted approval for GC-1 to clr them across 25R. GC-1 clrd them across 25R & told them to hold short of Rwy 25L. Aprx 32 sec later, LC-1 clrd Flt 866 for tkof. Later he said he had scanned the rwy & saw what he perceived as 2 Acft btn the parallel rwys. However, N98834 was still x-ing Rwy 25R as Flt 866 bgn tkof. The Cessna plt was focusing his attn on the Acft ahead & did not see Flt 866. Shortly after Flt 866 lifted off, its main gear hit the Cessna's vertical stabilizer. The Twr Cab Supvr was working a north Ctler's position while the Ctler was on a relief break. LC-1 was involved in other opnl errors on 12/21/85, 7/9/86 & 10/28/86.