Smart Lock is one of the new ways of handling lockscreen in Lollipop, simple that you’ve got Trusted devices that gives you quick entry into the phone.
This about when you have updated to Lollipop, it might already be there by default after a factory reset.
And you MUST have updated Google Play services, which the phone prompts for directly after the Lollipop update.
This all happens under Settings > Security
You NEED to enable a lockscreen with a password, pattern or PIN first or the rest of the steps will simply not work. I use Pattern myself since that is what I prefer. Smart Lock requires this.
If Smart Lock turns on. Then you’re done. If it doesn’t, you need to keep on reading.
Then you go down to Trust Agents that you find right under Advanced. Inside there you will find Smart Lock, simply enable that. And step back into Security where you now will have Smart Lock.