Dear Roger,
RINA is the Royal Institute of Naval Architects. However, given the information you have supplied, it sounds more like you are saying that this gentleman was a "designer" - an architect perhaps? - who was a passenger on both the Titanic and Lusitania, and who designed the buildings you have mentioned, and not a naval architect involved in the design of either ship. Is this correct? Or, are you looking for someone who had a hand in some aspect of the design of both ships but wasn't aboard either vessel?
At any rate, neither the passenger or crew lists for the Titanic show anyone named "Lockyear". There was one Edward Thomas Lockyer, a 21 year old grocer's assistant travelling in 3rd class; however, he was not among those who survived.
Regards,
Scott Andrews