Can I put an 01 lesabre motor in an 03 Century

Yes, History.......during that period the Regal and Century shared the same body but the Century did not come with the 3800 (the Regal did) with at said you can put the 3800 in your Century but you will need the engine control module from a 3800 and it might be best if it is from a Regal. You may need different motor mounts. I don't know of any source that will tell you everything that is different so hopefully you have time and extra $$ to make the change.