You can get a copy of his individual military service record via this link ....https://www.gov.uk/get-copy-military-service-records
... that should provide you with some basic information on dates, units, locations, movements, formations, etc.
You can also get copies of the regimental war diaries through the National Archives, which may give you information about his unit's time in Normandy and possibly the circumstances of his death ...http://www.nationalarchives.gov.uk/...ons-second-world-war/#4-unit-war-diaries
... there are researchers who will find and copy war diaries for you for a fee.
Here is an extract from the Lancashire Infantry Museum website telling abut the 5th battalion in Normandy ...By the end of June the 1st and 5th East Lancashires were also in Normandy, with the 53rd and 59th Divisions respectively. On 8th July the 5th East Lancashires took part in a renewed advance on Caen, during which their B Company fought an action at St Contest.
Both East Lancashire battalions then deployed into the close bocage country west of Caen. While the 1st Battalion held a succession of defensive positions in an exposed salient, at Cheux, Grainville and Bougy, the 5th Battalion were involved in offensive action 2-3 miles further west.
On 16th July (‘Black Sunday’) the 5th East Lancashires suffered some two hundred casualties in an attack at Fontenay-le-Pesnil. On 29th July the same Battalion made another costly attack, though this time with more success, and by 8th August they had advanced to the River Orne bridgehead at Grimbosq, where the 1st Battalion also crossed.
On 13th August, due to an acute shortage of infantry battle casualty replacements, the 59th Division, including 5th East Lancashires, was disbanded.