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He had a site saying he was THAT family fwiu. And at the time no one knew.
Source? Link?
He created business deals, got free loans, and tons more because of using their name.
The damage will be easy to prove, he stiffed many of those free loans and goods he got.
Damage to whom? Did Lev Leviev's family suffer ANY repercussions from Simon Leviev's (a.k.a. Shimon Hayut) actions? Whether now, or at any point in the past?
And like @PlatinumGuy say in many courts you don't need to prove damage to win.
To win what? In which jurisdiction? What remedies are available if one wins a defamation suit?
(as a side note, Lev Leviev's family are שומרי תומ"צ as far as I know, in a Din Torah even if damage could be proven, I am not sure that they could collect. I am definitely not an expert in Choshen Mishpot, maybe someone who is well versed could chime in).