ACR FLC REACTS TO TCASII RA FROM 2 VFR ACFT OFF DEP END OF LGB ARPT. PLT CONCERNED WITH LACK OF TIMELY TA FROM TWR LCL CTLR.

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DEPARTING RWY 30 AT LGB. CLRED ACFT X TO CLB TO 1500 FT; L TO 180 DEGS; LEVEL AT 3000 FT. CLBED TO 1500 FT; ACCELERATED TO RETRACTION SPD OF 193 KTS; LEFT FLAPS OUT AT 1.5 DEGS WITH AUTOPLT ON; STARTED L TURN. NOTICED 2 TARGETS ON TCASII. ON INITIAL CONTACT WITH DEP; THEY ASKED US TO VERIFY THAT WE HAD STARTED OUR L TURN. ATC THEN ADVISED OF TFC AT 10 O'CLOCK. LOOKING INTO THE SUN; COULD NOT SEE TFC. TCASII SHOWED TFC AT 10 O'CLOCK WELL LESS THAN 2.5 MI AND 400 FT ABOVE. WE WERE TURNING AND CLBING INTO THE TFC. I LOOKED TO THE R; OUT FO'S UPPER WINDOW. I COULD SEE TFC TO THE R AND ABOVE US; A CABIN CLASS TWIN CESSNA ACFT Y. IF I STOPPED TURN; WE WOULD HAVE CLBED INTO THE CESSNA TFC. LOOKED AGAIN AND DID NOT SEE TFC (ACFT Z) TO THE L. TCASII THEN GAVE AN RA AND CALLED FOR A CLB OF OVER 2000 FPM; WHICH WE WERE DOING. SEPARATION WAS ONLY PROVIDED BY TCASII AND THE BIG SKY THEORY. I QUESTION WHY LGB TWR CLRED US FOR A TKOF THAT PLACED US IN CONFLICT WITH ANOTHER ACFT RIGHT AFTER TKOF. FO BELIEVES UNSEEN ACFT WAS ONE THAT WAS IN CONTACT WITH LGB TWR -- HAD CALLED IN OVER QUEEN MARY AND WAS TOLD TO ENTER DOWNWIND FOR RWY 25R. I BELIEVE LGB TWR SERIOUSLY GOOFED UP IN CORING US FOR TKOF AND AT THE VERY LEAST SHE COULD HAVE ADVISED US OF TFC IN OUR IMMEDIATE DEP PATH.