Depending on whether the lookup is carried out when the page loads, or whether it's caused by a user action, you'll want to use one of the following events: 'onloadlookupfinished' or 'lookupcomplete'.

In the following sample, I'm setting the default value of a drop-down field that looks up all 50 US states to 'Arkansas'. The drop-down field has ID Field63. This particular lookup occurs when the page loads, so I use 'onloadlookupfinished'. The script waits for the lookup to complete before setting the default value.

$(document).ready(function () {
  $(document).on('onloadlookupfinished', function(event) {
    $('#Field63').val('Arkansas');
  })
})

This sample assumes that there's only one lookup on the page. If you have multiple lookups on a page, you'll want to check the triggerId of the event before setting a default value. The link above explains how to use triggerIds.