In business laws, filing a bankruptcy lawsuit refers to a case where a business entity claims bankruptcy in court. This is a common course of action for troubled companies and other entities willing to relieve themselves of some (or all) of their financial obligations, when they feel they'd be unable to comply with them given their current financial status. Filing for bankruptcy can sometimes be a lengthy and complicated process, due to a recent influx of companies that are using it for the malicious purpose of evading debts they're clearly able to cover.
However, a bankruptcy lawsuit can also have a slightly different meaning, when it refers to a lawsuit launched by one party in a bankruptcy to another, with relation to outstanding financial matters between them. For example, when a company files for bankruptcy, they can also launch a bankruptcy lawsuit as a creditor to another company, in order to legally free themselves of their financial obligations to that company. This normally has a different name, "adversary proceedings", and holds slightly different results for those involved.
Of course, companies aren't always freed of their financial obligations upon filing for bankruptcy. It if can be proved that the company is capable of covering their debts, then they're legally obliged to do so before the bankruptcy can be declared legal and start acting - most companies usually voluntarily declare their abilities to cover such debts though, and it's rarely needed to conduct investigations in this regard.