James, Encyclopedia Titanica has only this about him.
"Mr Patrick Lane, 20, was a resident of Limerick City, Co Limerick, Ireland. He was heading to New York City and boarded the Titanic at Queenstown as a third class passenger (ticket number 7935, £7 15s).
Patrick Lane died in the disaster. His body, if recovered, was never identified."
You may find more in a recent book called The Irish Aboard Titanic by Senan Molony. Senan is an Irish journalist and has combed local records very thoroughly.