If you are talking about Moto Display, which shows unread notifications that flash on the screen (or an unlock icon if there are no notifications), that's not the lockscreen. It's never been on Moto Display (or Active Display, which Motorola called it before that.)
It's actually too bad that Moto doesn't support something like that (i.e., owner contact info on Moto Display), but the good news is that anybody who never used a Moto phone before will just press the power button anyway if they find your phone. And there are more people in this world who have used a non-Moto smartphone than a Moto smartphone.