Try this.
Split up your event handlers. Use a global variable or if this is all wrapped in a function a private variable to store the rowid to use in the second event handler. It will work fine for you. You can optionally null the rowid in the second event handler also. Check out the fiddle
var rowid; //Global Variable to allow the rowid to pass between the two event handlers.
$(document).on("click", ".updateRecordButton", function(event){
//set global variable rowid
rowid = $(this).parents("li").data("rowid");
$("#displayOptions").popup('open', { x: event.pageX, y: event.pageY });
});
$(document).on("click", ".deleteRecord", function(event){
//use global variable rowid's value as a parameter to deleteRecord function
deleteRecord(rowid);
//optionally you can delete rowid here!
return false;
});