Maughold par register marriage has:
16 Apr 1906
Edward CLAGUE [aged] 26, Bachelor, Labourer, [from] Patrick, [father] Edward Clague (dec), Labourer, ~ and ~
Mary Ellen ROME 26, Spinster, Ramsey, [father] John Rome, Labourer.
I can't find Lily Clague's marriage in Maughold, but as Edward came from Patrick possibly there?
Also no sign in Maughold of William Parkes, constable, but there is this William Parker, constable, marriage:
13 Oct 1921
William Thomas PARKER, 37, Bachelor, Police constable, 36 Buersil Av, Rochdale, Lancs., [father] William Parker, Horse keeper ~ and ~
Frances PEARSON, 40, Widow, 8 Mona St, Ramsey, George Davis (dec), Collier.
Could Frances have died, and William Parker then married Lily?
Alternatively, a Lillian Mary CLAGUE aged 59, of The Terrace, Glen Mona, was buried in Maughold on 9 Feb 1947.
Brian Lawson's burial index has PARKES, Lily Selina 85 Dbc 22 Aug 1985. You could buy the death cert to see whether this was hers.