The 20 year period between the end of the first world war and the start of the second means that around 10 to fifteen infantry battalions could have been rotated through the Lucknow Garrison during the period. The rank of Rifleman helps to narrow things down a bit as only certain types of Infantry call their private soldiers by this title: mainly they are the Rifle Brigade, the Light Infantry and regiments whose title ends in Rifles, eg th Royal Ulster Rifles.
A quick check through some of the likely candidates for his unit shows that the 2nd Battalion of the Highland Light Infantry were stationed in Lucknow in 1930, although their overall stay in India spanned the period 1923 -1934. The 1st bn the Duke of Cornwall's Light Infantry were in Lucknow in 1927, and 2nd bn the Durham Light Iinfantry were in the North West of India during the period 1920-1936 so could have spent time in Lucknow. There are no records I am aware of which list the occupants of the individual barracks within the Lucknow District. Around 1927 - 30 the 6th Lucknow Brigade consisted of 4 infantry battalions at any one time.
As Cathy has already mentioned there is a death entry in the Army Overseas Death Returns in the period 1931-35 for an Edward T Richards aged 27 who died in 1932. The place recorded is Calcutta, but that may have been where he was in hospital after the incident. You can get a copy of the death certificate from the GRO to see if this gives further details which might confirm if this was your man. I would expect there to have been a Board of Inquiry into his death. This is somewhat similar to a coroner's Inquest in civilian life. Nothing comes up immediately on a TNA search for his name.
