Lloyd's won't typically carry deck plans.
A decent place to start is
http://www.mariner.org/library/selected-plans-drawingsIf it was a WW2 merchant sinking by a uboat, check
http://www.uboat.net/allies/merchants/ and see the details of the vessel, shipyard, etc. Then you can consider visiting one of the many NARA (National Archives) locations for possible plans. You can contact one or more of these forums and ask...
http://www.pcez.com/~artemis/NASAlinks.htmYou may even get lucky on Google books or Google images.
There's no "right" way to find ship plans, but with persistence, you'll discover more avenues.
Most of the steamers built in the early 1900s were very similar. Tramp steamers, Hog Islanders, Ocean Class, Liberty's, etc had a basic layout common to each other with a few variations in the centerhouse arrangement. Let me know if I can help.
All the best,
Darren