If this person is your ex there's no reason for you to be involved in one another's dating lives. I think continually spying on each other's profiles is detrimental to your relationship and will impede on your ability to form a friendship, if that's what you both desire. I don't know if the two of you had some time apart after you broke up, but sometimes jumping straight into a friendship with an ex makes things hard. It's necessary to take the time to individuate your life from theirs before trying to become friends again, and it sounds like you have done that yet. It might be a good idea to take a bit of a break from each other's lives, especially if you think he's coming by and then lying about it. That shows an unhealthy involvement and an unwillingness to let go on his part. It can't hurt to take some space to sort things out for both of you.