This name is meant to be pronounced el-ee, like ellie, and sounds much nicer that way, of course its (mispronounced according to its origins) English version of ee-ligh is fine although it is reminiscent of the farm yard song 'ee aye ee aye o'.
Everyone I know pronounces Eli, Elijah, Elisha with a distinct long E. And then LIE as heard in "Do not LIE to me about your report card, Eli."Also, I prefer it to be a nickname for Elijah or Elisha rather than a given name, because the Eli in the Bible was an old, fat, lazy man.