Ok, Just gone through my books and found the following, The 1st order for 500,000 guns was received in January 1942, they gave them selves 5 weeks to train the increased work force so that takes them to mid Feb. The first order was completed with in 1 year so they had reached gun Serial number E5 (1-99,999 A1-A99,999 etc.) by approx Feb 1943. A second order for 500,000 guns was awarded to LB, however this was cancelled after 376,794 guns had been completed
They were producing 1500 guns per day at that time so if I'm correct, your gun would be from the first week in April (Give or take) 1943.
Total LB production was 876,794 although official records state 876,886, a 92 gun diffrence. So the last serial number produced should be G76,786 or G76,878 which would make it Mid Sept 1943.