You have an ASP.NET ListBox and you want to be able to allow users to Double Click on the list box to select items.  You can add a hidden button to your page and then add a double click event to the list box to select items as shown below.

//Setup a string that will call a hidden button click event
string BntListBoxClick =  "document.getElementById('" 
                               + BtnAddToTarget.ClientID.ToString() + "')" 
                               + ".click();";

//Add the double click event to the list box
LBoxSelectItems.Attributes.Add("OnDblClick", BntListBoxClick);