FLT CREW OF LJ35 AND CLE TRACON DISAGREE AS TO APPROPRIATE DEP PATH FROM RWY 23 AT LNN.

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DEPARTING LNN ON RWY 23 WHICH HAS AN OBSTACLE DEP FROM THAT RWY; WHICH STATES (ON COMMERCIAL CHART AERODROME SIDE) 'CLBING L HDG 180 DEGS UNTIL 1300 FT; THEN AS CLRED.' ON THAT IMC MORNING ON THE RWY; VIA CELL PHONE; RECEIVED A CLRNC FROM FSS THAT READ 'CLB HDG 320 DEGS; MAINTAIN 2000 FT; SQUAWK XXXX.' IN CONFLICT WITH THE OBSTACLE DEP. NOT FAMILIAR WITH THE TERRITORY; MY CO-CAPT AND I DISCUSSED PRIOR TO DEP THAT WE WERE GOING TO USE THE OBSTACLE DEP FOR RWY 23. WE WENT IN FRONT OF THE HANGAR TO VIEW 2 SMOKE STACKS WHICH WE COULDN'T SEE DUE TO POOR VISIBILITY AND CEILING. HE SAID 'WELL; THE WX IS TOO BAD TO SEE THEM AND OUR COMPANY PROC FOR DEPARTING IMC ON RWY 23 IS THAT OBSTACLE DEP PROC AND ZOB IS GOING TO YELL AT YOU; BUT THIS IS WHAT WE DO EVERY TIME WE DEPART RWY 23 IN IMC.' SO WE DEPARTED; FOLLOWED THE OBSTACLE DEP AND; SURE ENOUGH; ATC ASKED 'ACFT X; SAY HDG.' RESPONDED WITH 'DEPARTING LNN VIA 180 DEG HDG TILL 1300 FT AND IN THE TURN TO 320 DEGS.' ATC; 'THAT'S NOT [WHAT] WAS ASSIGNED.' WE WERE THEN QUESTIONED BY THE FOLLOWING CTLR 'WHY WERE YOU ON A 180 DEG HDG?' I RESPONDED WITH 'OBSTACLE DEP FROM LNN RWY 23.' ATC; 'WHEN YOU GET ON THE GND; CALL THIS NUMBER AT CLEVELAND APCH.' ONCE ON THE GND; SPOKE WITH ZOB. WENT THROUGH THE STEPS WITH HIM AND HE COULDN'T UNDERSTAND WHY WE DID WHAT WE DID. HE REFERRED TO GOV CHARTS; I REFERRED TO COMMERCIAL CHARTS. I SAID 'THEY SHOULD SAY THE SAME THING.' NO ACTIONS TAKEN AGAINST ME. FOLLOWING MORNING; SPOKE WITH MY DUTY OFFICER AND HE MADE A CALL TO CLEVELAND. THEY HAD REVERSED THE DECISION AND SAID THEY WERE WRONG AND I WAS CORRECT.