EMB120 FLT CREW HAS RWY INCURSION AT LFT.

Narrative

AT XA18Z WE RECEIVED ASOS AND IT RPTED TWR CLOSED. AFTER START-UP; WE ANNOUNCED -- TWR/CTAF THAT WE WERE GOING TO TAXI FROM THE TERMINAL TO R FOR DEP. WE MADE 2 CALLS BEFORE LEAVING THE RAMP; WHILE TAXIING OUT; WE CROSSED RWY 4L AND HOLD SHORT OF RWY 4R WHILE AN ACFT WAS LANDING ON RWY 22L. AFTER THAT ACFT LNDG; WE AGAIN ANNOUNCED THAT WE WERE GOING TO BACK TAXI RWY 22L TO DEP ON RWY 4R. TWR THEN ASKED US IF WE TALKED TO GND PRIOR TO TAXI. WE SAID NO; THAT WE THOUGHT THE TWR WAS CLOSED. HE INFORMED US THE TWR OPENED AT XA30Z. WE APOLOGIZED TO HIM; AND TOLD TWR THAT WE MADE 2 CALLS BEFORE LEAVING THE RAMP. TWR SAID HE DID NOT HEAR US AT ALL. TWR THEN GAVE US OUR IFR CLRNC AND CLRED US TO BACK TAXI DOWN RWY 22L/4R. THE FLT CONTINUED TO MEJ WITHOUT INCIDENT. THINKING BACK ON THE SIT; THE FIRST MISTAKE WAS NOT NOTING WHAT TIME THE TWR OPENED ON ASOS. I AM NOT SURE WHY TWR DID NOT HEAR OUR XMISSIONS. HE MAY HAVE BEEN WORKING MULTIPLE FREQS. I AM NOT SURE; BUT HAD HE HEARD US; THIS SIT WOULD HAD BEEN AVOIDED. WE HAD ALSO BEEN ON A CONTINUOUS DUTY OVERNIGHT; AND HAD ONLY ABOUT 4 HRS AT THE HOTEL THAT NIGHT. I AM SURE THAT CONTRIBUTED A LITTLE TO THIS SIT ALSO. IF YOU HAVE ANY QUESTIONS; FEEL FREE TO CONTACT ME. I ALMOST FORGOT -- WE LEFT THE GATE ONLY 8 MINS AFTER TWR OPENED UP.