In the closes big town that has a few lawyers, the matter at hand here is not about cryptocurrencies, it's about a foreign financial regulated company holding your funds and denying releasing before verifying your identity, you simply need a lawyer who has basic experience in debt collecting, even if it's a reverse case the procedures should be familiar to him.
Will you go to court and say I tried to fake my identity documents and I got caught by the staff of localbitcoin and they closed my account .
That's not how things work!
Using a fake identity is a crime but LB is not the police, they can only forward this information and with it the BTC, if the authorities ask for the seized funds. They can't help themselves with some funds, especially if those are involved in a case of forged identity, they will also face a criminal charge if they do so. What OP has done is a separate case, no matter what punishment he might face if he is found guilty by a totally different court for his fake papers his possessions are still his until a judge declares otherwise, and no way in hell while those funds be awarded to LB.