Passing a parameter to function with single quote

You can escape quotes/characters by prepending \ to it:

var string = 'my string with "double quotes" and \'single quotes\'';
var string = "my string with 'single quotes' and \"double quotes\"";
//                                               ^              ^

Using a dynamic string:

var foo = "bar with 'quotes'";
var string = 'my string with "double quotes" and ' + foo.replace(/'/g, "\\'");
//my string with "double quotes" and bar with \'quotes\'

You can escape it using \:

var htmlAnch='<a onclick="javascript:selectEmployee(1100,\'Lauren O\'Donald\');return false;" 
             href="javascript:void(0);">O\'Donald, Lauren</a>';

However as you've tagged this question with jQuery,a better solution is to hook up an event to the element and use data-* attributes to store the relevant information, which will avoid the use of ugly onX attributes. Try this:

var $htmlAnch = $('<a />' {
    text: "O'Donald, Lauren" ,
    data-id: 1100,
    data-name: "Lauren O'Donald"
}).click(function(e) {
    e.preventDefault();
    selectEmployee($(this).data('id'), $(this).data('name'));
});

$(document).append($htmlAnch);