I think the man you are looking for is likely to be 1757 Gnr Richard Kavanagh.
His Medal Card is on Ancestry (specifically stating "Not identical with 195608"), and there are some papers in the Service and Pension records too. These records confirm he served with 1st West Lancs Bde and show he enlisted in Aug. 1914 and was discharged unfit in Sept. 1916 with nephritis.
Comparing his family details from these records with the censuses etc., he would appear to be Richard William Kavanagh, born West Derby Q1 1879, married Frances Hewitt Q3 1900 ... and quite possibly died at West Derby Q4 1916, aged 37 (Kavanagh Richard W, Vol. 8b Page 506). The age fits! Ancestry's Liverpool burial records show that he was buried at Yew Tree Cem on 1/1/17 (grave no. 4B274).
You'd probably need to order the death cert to be certain that this death is the same man, but if the DC positively links the death to the service record, then there might be a case to have him belatedly commemorated by CWGC - as he should be if his death was attributable to his military service. The In From The Cold Project can help with that:
http://www.infromthecold.org/Adrian