does a change order extend the time of the contract to file a lien

The critical date is the day you were last out there performing work in furtherance of the contract, as modified by change orders. However, this last day needs to be a day you were performing substantial work under the contract, not just punch out or warranty work. So if the change order was for something small, then it might not count to extend your deadline. Further, if the contract was not authorized under the contract, then you may also run into issues with the lien. My suggestion is that you contact an attorney to discuss your options and timelines. 

So long as the Change Order was substantive scope work, and not punch list and/or clean up work, you would base your lien timing off the date you completed the Change Order work.  

You go by the date you LAST performed work on the site, which includes work pursuant to an approved change order.