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The suit says the deal could help Blackstone tighten its grip on the management of $25 billion in insurance assets.
Blackstone says that is a "total misreading" and its client has the independent right to cut ties.
Read Insider's original investigation into Blackstone's lucrative deal with the chairman of Fidelity National Financial.
Managing money for wealthy clients and institutional investors can be a cutthroat business, with competitors vying to steal accounts and undercut their rivals' fees. And yet the world's largest private-equity firm, The Blackstone Group, seems to enjoy an uncanny level of job security: According to claims in a recently unsealed lawsuit, it has struck a deal with at least one major client that makes it almost impossible for the company to get fired.