egopay is a joke runned by amateurs.
also, egopay transfers should be final so Lakebtc must credit your account. put pressure on them. you already gave them your funds which are not reversible(according to egopay terms)
it is not your concern what kind of problems LakeBtc does have with Egopay and neither about any Egopay stupid rule.
they did not inform you about that prior your transfer so, LakeBTC MUST fund your account otherwise they will proof to be like Egopay amateurs from which everybody is running away.
I think Egopay is easy and fast, just like a middleman, I put the money in there, I can always get it back quickly.
But that like you said, all on the premise is that Egopay won't run away.