Track # in Lexicon is a number you can change yourself, it does’t have anything to do with the order of tracks. Track # is the 01 thing you usually see on CDs.
If you want the original order of the playlist (so the same as your Engine screenshot), you have to “unsort” the playlist. You can do that by clicking the header where the sort arrow appears, until the arrow disappears. Then it is in the original order.