Lampeter wasn't founded until 1822, admitting its first students in 1827 - was this too late for Richard Pughe?
There are a couple of Richard Pughe records in Alumni Oxonienses who might be your man: if you know his age at death a cross-reference would be possible. Most likely one is Richard, son of Richard, clerk [= clerk in holy orders, so a family in the Church?], of Llanegryn, co Merioneth; matriculated March 1812, aged 19; Jesus College.
CCEDB has him appointed as Rector of Llanfihangel-yn-Gwynfa, with a BA degree, on 23rd July 1823. It says the Patron was the Bishop of St Asaph. The vacancy occurred because of the death of the previous Rector, James Hamer.