If he tells you he has feelings for you then it's not on that he is now seeing someone else - perhaps he is trying to get a reaction. Although because I'm not sure of the timescales (when he last said that he was lonely and missed you against when he started seeing this other person) I think only you can be the judge of that.
With regard to seeing other people, depends on the dynamic of your relationship now. If it's a kinda - we tell each other everything because we see each other like really good mates, then fair enough. But if not, he is your ex. What hold do you have to know that kinds stuff? And why does he have to tell you?
That said, you have asked and he has lied about it. Perhaps you should ask him why he hdid that. And at the same time, if he has said he still had feelings for you during the time he's been seeing her, why he's done that too. 'Cause that's not fair on the other lass.