I think some other connections between the three, are their parents. Eowyn's parents died, Boromir's parents died (yes his father died after him, but he died). With Gollum, his own family kicked him out.
In Boromir's case, a reason for his glory lust, and valour, could be Denethor. Denethor saw Boromir as Gondor's only hope left, and put a lot of pressure on him. Eager to please his father, and to see Gondor victorious, he feels the only way to do that is through the Ring.
Eowyn's parents died at a very young age, Boromir's mom died when he was young, his father was a good strategist, but a bad parent, and Gollum, as mentioned was shunned by his own family. So, none of them have this strong relation with their parents.
I'm not sure about Gollum, but in Boromir and Eowyn's case they have people to help them out. With Boromir, it's Faramir, who he's always looking after, and as it states in the appendix, despite the father's favortism they rarely fought. Eowyn has Theoden she's looking after, and Eomer is looking after her. I'm not sure where Gollum fits in, because he really doesn't have anyone, except the Ring.
This is just some of the my thoughts, with the three characters parents, it could quite honestly lead to no where.
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