The brass shoulder may hold a clue - it looks as though it might end in 'A', in which case it would be a branch of the Artillery, who also wore a white lanyard on the left shoulder at WW1 time.
There are ten Lloyds with a first name Henry listed among the medal index cards for Artillery men. It should not take too long for you to list them from the National Archives, Documents Online site, or from Ancestry, and then use those regimental numbers to search Ancestry's military records which are free to all, today, but probably not tomorrow.
A