What was your father's name? Birth year?
There were a GREAT many ships that had names that ended with "Lyckes," for the good reason that there was a major shipping line name Lykes Brothers Steam Ship Company, later known as Lykes Lines, that was in operation as recently as 2005. For a list of ships owned and operated by Lykes Brothers, see http://www.theshipslist.com/ships/lines/lykes.shtml. The list includes a ship, actually two ships, named JOHN LYKES. One, in which your father probably served, was built in 1941 and scrapped in 1972 or 1973. The second was built in 1960 (by which time the first ship may have been sold and renamed) and scrapped in 1995. Also see http://www.shipbuildinghistory.com/history/shipyards/2large/inactive/federal.htm (scroll to hull number 176) and http://www.shipbuildinghistory.com/history/shipyards/2large/active/ingalls.htm (hull number 473) for slightly more information on both ships, including where they were built.
But identifying the second ship with just its last name is a hopeless task under the circumstances. A better approach may be to try to obtain your father's military service records, which should give the names of the ships to which he was assigned. See this page within the Armed Guard website, http://armed-guard.com/searchmil.html, in particular section II.A.1 - Records of Individuals, Military, for instructions on requesting a copy of his records. You will have to contact the National Personnel Records Center in St. Louis, MO, and provide as much identifying information as you have (name, date and place of birth, date and place of death, Social Security Number, military ID number ["serial number"] if you have it, etc.). The page has links to all of the information you will need to request his records, including a required form. There will likely be a charge for researching, photocopying and mailing the records but the Records Center staff will alert you to the cost before beginning work. The information from his service record will likely be more extensive than anything you could find by asking here. Once you have his records and if you have any more questions, come back and ask them.
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website