I want to clarify something, because I feel it's misunderstood (correct me if wrong). He's not suing what was his own lawyers. Here's the setup.
1. He signs a binding agreement with Twitter in April 2022 to buy.
2. Gets cold feet due to lack of investors, tech stock prices coming down after a period of hype, climate of expected impending recession, and rising interest rates... or... maybe he never thought he has to actually buy Twitter because the agreement was a formality he can ignore.
3. Starts finding reasons to get out of the deal, i.e. the infamous argument about how many bots Twitter has (and whether this constitutes material change in what Musk agreed to buy for that price).
4. Twitter (not Musk) hires the firm in question "Wachtell, Lipton, Rosen & Katz", to ensure Musk follows the contract. Twitter hired that firm. They were playing against Musk's intent to get out of the deal.
5. So they do their job, and Musk can't get out of the deal. And Twitter pays them 90 million as Musk acquires the company.
6. Now Musk is mad that what is now his company paid 90 million to fight against him. And he's fighting to get some of that money back, claiming "Wachtell, Lipton, Rosen & Katz" overcharged Twitter because Twitter new after the deal, this counts on Musk's bottom line anyway.