A corrupted entity that was once a protector of Lemon's world but has been twisted by dark magic. This entity would be jealous of Goku's pure power and would want to absorb it. It would also see Lemon as a traitor for teaming up with an outsider like Goku. So it would be constantly attacking them, using its knowledge of Lemon's world's secrets and its own dark powers to try and defeat them.
Maybe an interdimensional warlord who sees Goku as a threat to his conquest plans and Lemon as a valuable asset. He would stop at nothing to capture them and gain their powers. He could have an army of minions from different dimensions, making it really challenging for Goku and Lemon to fight back. This antagonist would be very cunning, constantly devising new strategies to outwit our heroes.
Maybe a mad scientist - type character who has created a device that can disrupt the fabric of reality. He wants to use it to reshape the universes to his own liking. Goku and Lemon get in his way because they are trying to protect their respective homes. The scientist is constantly evolving his device and creating new threats for Goku and Lemon to overcome.
It could be a lemon - loving pirate who has a grudge against Luffy for some reason. Maybe Luffy accidentally destroyed his precious lemon grove on an island. So this pirate, with his crew of lemon - themed fighters, constantly tries to sabotage Luffy's adventures and steal his treasures.
Maybe a giant lemon - themed monster. This monster is created by some dark force that wants to disrupt the balance between the two worlds in the crossover. It has the ability to spit out acidic lemon juice that can corrode anything. Ichigo has to figure out its weakness and defeat it to restore peace. The monster could be controlled by an unseen force that is the real antagonist behind the scenes.
In a crossover with the Bleach universe, Aizen Sousuke could be a formidable antagonist. His intelligence and powerful abilities would make him a tough enemy for Goku. Aizen could manipulate situations to his advantage, and Goku would have to use his fighting instincts and newfound knowledge of this strange world to defeat him.
It could be Zamasu. Since Goku Black was Zamasu in Goku's body in the original story, perhaps a more powerful and enraged Zamasu could be the main antagonist. He might be jealous of the new fused form's power and seek to destroy it.
Frieza would be a great antagonist. If Goku goes back in time to a point before Frieza was defeated, Frieza could be an even more menacing force as Goku might not have all the power - ups he had in the original timeline. He'd have to rely on his wits and basic training more.
A new character could be the main antagonist. For example, a powerful alien who has heard of Goku Black's reputation and wants to prove himself by defeating the reincarnated warrior. This alien could have unique powers that are a challenge for Goku Black to overcome, like the ability to nullify ki attacks.
If it's a crossover with Alice in Wonderland, the Queen of Hearts could be the main antagonist. The Queen might see Tinkerbell as an intruder and try to behead her. Tinkerbell would have to use her wits and magic to survive in the crazy world ruled by the Queen of Hearts.
Another option for the main antagonist could be Beerus. As a God of Destruction, he wouldn't be happy with Zamasu and Goku Black causing chaos. Beerus is extremely powerful and has the authority to deal with threats to the universe. He might see their actions as a direct challenge to his power and order. If he gets involved, he could completely change the dynamic of the story, as his power level is on a whole different scale compared to most characters in the Dragon Ball universe.
It could be Orochimaru. He's always after power and seeing Naruto with Son Goku's power would make him a prime target. He might try to extract the power from Naruto for his own evil experiments.