Lakshman Kumar willing to marry Balaram's daughter is another story (although it is not in any Puran rather is just a forklore) Duryodhan was Balaram's favorite shishya. He had earlier arranged his marriage with his sister Subhadra, but Subhadra eloped with Arjun and their alliance could not happen. The next time he decided to get his daughter married off to Duryodhan's son, the alliance was fixed, but Sasirekha loved Abhianyu since childhood (remember Abhimanyu spent his childhood in Dwarika (with his monther Subhadra) when the Pandavas were in exile, Subhadra had then gone to her Mayka.
Krishna ji knew that both Sasirekha and Abhimanyu loved each other, so he with the help of Ghatochkat made the lovers unite. This story actually is no where documented and is in much probability false (one might argue that Arjun married his first cousin, but cross cousin marriages were not very common those days especially in Chandravanshis, Yaduvanshis(who were considered lower to the pure line Kshatriyas) on the other hand did follow this practice, (it is probably due to this reason that it was Subhadra who loved Arjun before marriage and not vice versa, probably he could not have even thought about Subhadra in those lines. I would definitely not even think of my Bhaiyaa, my bua's son on the terms of getting married), also in this story Lakshman was shown as a stupid ugly fellow, which he certainly wasn't. He might not have been a great warrior, but was still good enough
Lakshmana and Saamb story (yes it is Saamb and not Shyam which is one of the names of Krishna ji) is a more authentic one as it finds its mention in the Bhagwat Puran. Saamb was the so of Krishna ji and his second wife Jamwanti. (Pradyumna as you said was the son of Krishna ji as well but he was from his first wife Rukmini) had started loving Lakshmana who was the twin sister of Lakshman Kumar and a very beautiful girl. Saamb was a very beautiful person, in a female attire he could easily give challenge to the most beautiful girls of those time. Lakshmana also had some liking for the Yadu prince but it was not as great as to elope with him. Saamb decided to abduct this girl and take her to Dwarika, but while he was leaving for Dwarika, the soldiers of Duryodhan caught hold of him, and Duryodhan arrested Saamb. When this information reached Dwarika, both Krishna ji and Balaram got anxious and the latter decided to attack Dwarika, Dury as I already said was Balaram's teacher, so he went to him. Balaram loved Saambb dearly and so he asked for Saamb's immidiate release and marriage of Saamb and Lakshamana to which Duryodhan readily agreed. Saamb and Lakshamana was said to be a very lovey dovey couple in fact
wow..that was quite insightful...thanks a lot..