At least he's giving the impression that he's not stalking her, but I don't feel too certain about it, at least not after his strong reaction after he found out about Ian and Lena. Axel and Seymour showing up together at the restaurant, Axel posing together with Lena at the photoshoot with Seymour … that could be coincidences – or it could be intentional, but made to look as coincidences. But even if it's the latter, it's difficult to say if it's only Seymour who's doing the scheming and using Axel as a prop in his grand plan, or if Axel also has a hidden agenda. My theory is that Axel is at least partially involved in Seymour's plan – that Seymour's told Axel that if he does as he's instructed to, he'll make sure Axel'll get Lena back. But that's obviously just speculation.
Personally I don't believe that Axel is scheming - at least not in the way mentioned here. I do believe that there's a very good chance Axel is still in love with Lena, and in fact, may have only truly realized he loved her when/after he lost her. If that was the case, of course he would be tempted to try things to get her back, and also be unable to resist taking the opportunity in that photoshoot (which was suggested to him btw - he didn't instigate it). But maybe all that is just wishful thinking on my part. I do feel there is more to Axel then the simple lens of 'cheater' that we're kinda forced to see him through via Lena right now.
Now, whether Seymour is scheming is another matter entirely, because while (if I recall correctly) Axel was surprised when Lena showed up for Seymour's photoshoot, Seymour seemed less phased about the fact that Lena and Axel used to date, and felt very comfortable testing Lena's boundaries when Agnes suggested Ian join her in the photoshoot (remembering that Agnes didn't know that Ian and Lena were a thing). Perhaps he was curious to see what would happen if they shot together, or much more likely (and in vein with his personality), saw an opportunity to test Lena's drive and professionalism in the face of an awkward and intimidating situation.
Also, although we have seen Axel casually flirt with Cindy, he's never straight up come on to any characters in the story so far, and anything more was just Ian's speculation that Axel would do it based off of his impression of Axel as a total lady-killer.
If Axel fucks Cindy at some point, perhaps it will only happen if Lena has made it clear there is nothing between them anymore. At that point he could slowly come to terms with the fact that it was over and move on, seeing no reason not to fuck Cindy when she shows an obvious interest in him.
Of course finding out that Ian was with Lena is gonna cause a strong reaction in Axel, and I think that would happen regardless of whether he still loved Lena or not. If he loves her it goes without saying, but if it's over and he's trying to move on... well, some guys still get a bit weird knowing of or being in the presence of a guy who is currently boning the girl that they still have residual feelings for. Seems pretty natural. At least he didn't fight Ian right there and then (which means potential for an Axel-Ian friendship! Yay).
The reason why a lot of people suspect Axel will show up when Lena travels home, is mostly that he's the only character (maybe in addition to Ivy) that has any relationship to her parents. And we also know that Lena's mother recently talked to Axel, and at least partially suggested to Lena that they should get back together. But if she's at the hospital and seriously sick, I guess it seems a bit far fetched that she uses her time to plot a plan to get Lena to meet Axel again. Except if she's decided that she needs grandchildren right now, that is.
Didn't Axel actually go to lunch with her parents? Maybe I'm mis-remembering it, but I'm pretty sure it wasn't
just talking to Lena's mother. To me that sounds like Axel still has some decent connection with Lena's parents, though his exact motivations are still unclear. In relation to that, we also still don't know the full story about just what Axel and Lena's relationship was like, but we'll probably find out in chapter 9.