CLOSE PROX ACR-LGT ON A VISUAL APCH TO NAS AND ACR-LTT MAKING VFR CLIMB FROM NAS.

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PROCEEDING ON 160 DEG HDG TO NAS AT 1500'; WERE CLRED FOR VISUAL APCH TO RWY 27. WHILE IN SEMI-DOWNWIND APCH TO RWY 27 AND ON TWR FREQ; WE ENCOUNTERED LTT SEA PLANE AT 1100 AZIMUTH AND AT OUR ALT ON A COLLISION COURSE. CAPT WAS FLYING AND TOOK IMMEDIATE EVASIVE ACTION WITH A STEEP RIGHT TURN TO AVOID COLLISION. LTT MADE DIVING RIGHT TURN BEHIND OUR ACFT. APPROX DISTANCE AT 300'. CAPT AND F/O WERE INVITED TO NAS APCH CTL ROOM FOR AN EXPLANATION. CTLR OVERSATURATED AND DISTRACTED BY ANOTHER POTENTIALLY HAZARDOUS SITUATION CAUSING HIM TO OVERLOOK OUR CONVERGING TFC. LTT HAD DEPARTED PARADISE ISLAND ON A SW COURSE VFR. WE BELIEVE CTLR WAS NOT AT FAULT AND THAT LTT VFR DEPS SHOULD BE REVIEWED. SUPPLEMENTAL INFO FROM ACN 85096: I WAS PIC OF SCHEDULED SVC FROM WZY TO FLL. THE FLT WAS CONDUCTED UNDER VFR AND CONDITIONS WERE CLEAR WITH UNRESTRICTED VIS. WE DEPARTED WZY TO THE W; CLBING THROUGH 500' ON A 300 DEG HDG. RADIO CONTACT WAS MADE WITH WZY DEP ON 121.00. DEP CTL ISSUED TRANSPONDER CODE. AFTER CLB CHK WAS COMPLETED AT APPROX 1200'; CAPT OBSERVED AN LGT OFF OUR RIGHT WING. HE IMMEDIATELY TOOK CTL OF THE ACFT MAKING AN ABRUPT CLBING RIGHT 45-60 DEG BANK TURN. THE LGT SIMULTANEOUSLY MADE A RIGHT DSNDING TURN; PASSING OFF OUR LEFT SIDE AT APPROX 100'. AT NO TIME DID ATC PROVIDE US WITH ANY TFC INFO; AND FURTHER INQUIRY TO ATC AS TO THE TFC WE HAD EVADED PROVIDED NO INFO.