This is spoiler yaa
For provoking Nunnaly, the reason is like this.. It's been mentioned in the newest chapter 10 about 'pestokraive', it's when all magic energy inside powerful magician burst out and cause accidents, usually caused by emotional outbursts. Since child, Lockmann has powerful magic so he had a really serious case of 'pestokraive' and burned things accidentally. Nunnaly actually has powerful magic too, it was hinted early when her hair change from brown to light blue. So Lockmann provoked and made her mad constantly as to make her use magic so her magic flows regularly (and not in sudden accidental burst).
For Lockmann being a player, ehh.. it's true he's a playboy though. But if it's about the law thing.. From previous chapters, when Nunnaly's senpai explained about Prime Minister Cucumberly(?). He made laws so that the commoner he loved lived easily. One of the laws is that noblemen cannot make working-class women a 'mistress' or 'lover'. Even if both sides agree and have mutual consent, it is forbidden. So if it's not 'official wife', noble x commoner is a no-no.
But even if Lockmann wants to marry Nunnaly, he can't. Lockmann is part of royal family, since he's the King's nephew, thus he and Prince Zenon are cousin. It can be said that Lockmann is in line for the throne. And as you said, royal family cannot marry outside of nobility. It is a LAW. The aristocracy keeps a strict tradition that royalty x commoner cannot happen at all costs because royal bloodline purity is a must.
Lockmann can make harem if he wants, as long as the other side is part of noble. Since Lockmann is a noble and part of royal family, he getting together with a commoner is a big NO. He'll breach the law, and it can be considered as a crime.
But several of the girls he has had relations with were commoners.. thats why i doiont get it.. that was ok but Fl isnt? And even the king is ok with their relationship.. so its only the nobels that arnt.. if his father could change the law for his wife... why cant Ml for FL? It makes almost no sense as his blood is already not "Pure" like the nobels wanted.
Was he? Honestly, I couldn't tell apart which nobles and commoners from Lockmann's mob fangirls. As far as I know, Lockmann is flirty with many girls and doesn't reject any girls who come to him, but he's still single and not in any romantic relationship.
And the one who changes the law is not Lockmann's father but the previous Prime Minister from 200 years ago or so. It hasn't been mentioned, but I assume that Lockmann's mother is a noble, while his father is the King's younger brother.
Eehh.. no worries, Lockmann slowly plans to make his moves and working hard in his way. Later there's a big war (with demons? I'm not sure), and the King will reward anyone who contributes. So Lockmann's request is freedom of marriage to anyone he choose.
One more thing, it was lockman who cast the magic barrier in his house and gave access to the FL to enter...........That is why lockman's father told FL to come to the Ball in order to see what is son going to do and he even mentioned that FL is good for this roll because despite being noble he still allowed FL to enter
So some of the spoilers justify the Ml's behavior, but those justfications make no sense!
Spoilers and reasoning below:
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First time justification and reason it dosn't make sense:
So we all know Ml prety much fell in love with Fl at first signt in the Academy, but spoilers state that Ml began bulling Fl to get her to stay away from him (he is a member of the royal family and they have to keep the bloodine pure so can't marry just anyone).
Ml starts to bully FL to get her to stay away, but Fl does stay away! She starts to avoid Ml and avoids interating with him! Yet he seeks her out and starts to use his fire magic to get her to react and retaliat (he makes her interact with him....) IF he was trying to get her to stay away why is he forcing her to physicaly retaliate?!?! That makes no sense...
Also he purposfully makes Fl become his rival by taunting and teasing her everytime she does worse than him, again Ml is causing Fl to be close to him.
His reason to bully is directly caused by his own action of not leaving FL alone when she ignored him..
ML is a renown "Player" in high society!:
So it has been stated in spoilers that because Ml is of Royalblood he cant just marry anyone he wants, but it was never stated that he cant be in a relationship!
At the Academy he was a renown Playboy dating and flirting with most girls exept Fl (it may be justified because at the Academy they were all Equals).
However the Ml is still a rumored Playboy said to have several lovers and be engaged to the princess! If the Royalblood line was so important... how come this is alowed? and yet a relationship with FL isnt?
This makes no sense, Ml is alowed to openly flirt and kiss several women in public yet cant say he likes Fl despite him being able to say he likes all the other women?
Second time the reason does not add up:
When Fl and her friend acidentaly teleports to Ml's home.
Fl ends up inside the mansion and her friend ends up outside the mansion, Ml tells Fl the reason she was inside and her friend is outside is because of the protective Barrier around the mansion (anyone not given acces by the family head can not enter).
Fl has been given acces to enter the mansion barrier form Ml's dad despite never having met him...
Fl gets informed of the upcomming ball the Ml's mansion and goes back home, yet ML's father shows up and offers her a job, despite yet again him not knowing her other than from ML's mentions of her. And the job is to act like a guest at the ball while looking for posible trouble, so she is to working as security despite the family having a personal guard and her only being a receptionist!.
It is already made clear that Ml has told his dad about Fl when he was back at the academy, but after the Ml's dad saw Ml's interactions with Fl.. it became clear to him that Ml might have feelings for her! So Ml's dad asks Fl to do the job to have them meet.
The third reaon, the Ml's dad:
The Ml's dad went all the way to Fl to offer her a job to work as security during the Ml's engagment ball, the father also states that Ml accepted the engagement to the princess but that he is interested in his sons love life because he himself married for love and not bloodline!(this is a big hint).
Fl accept the job and Ml's dad drages her in for a makeover, makeup, expensive dress, jewlery, a wig and a mask (its a mask ball). Fl confused as to why this was neede gets told to blend in... The King comes out at the ball and anounces the "Ball Game of find Ml", the King says that Ml and the princesses love seems so strong but that true lovers can find each other even when blindfolded.
Ml finds Fl right away.. (proving to the King and ML's dad that the ML loves Fl and not the princess).
SO as said above .. The Royalbloodline is just an exuse used by Ml... This is proven because his father(the King's brother) could marry out of love!.. so why cant the ML?
It is obious that the Ml's father wants the Ml to marry out of love not Royalblood purity and so does the King hence the reason for the Ball Game. The father and the king woried that Ml was only marrying because to duty and not love!..
So ... nothing is preventing Ml from getting together with Fl, the only thing that can make him marry for Blood purity is an order by the King and yet the King made the Ball Game to test if the Ml was marrying for love or duty!
No where is it shown that the King wants and expects Ml to marry the princess...
its all just the Ml's own reasoning...