If there is a lawsuit filed against more than one party and that party is the only person filing bankruptcy, there are two possible scenarios depending on which chapter of bankruptcy is filed.
In a Chapter 7 bankruptcy, the other defendant(s) are not protected, and the lawsuit may continue against the other defendants without delay.
In a Chapter 13 bankruptcy, the other defendant may be protected (and the lawsuit stopped) if the lawsuit concerns a consumer debt. If the lawsuit relates to a non-consumer debt (like a business debt) then the other defendant(s) are not protected.  Even if the lawsuit concerns a consumer debt, the plaintiff can ask the bankruptcy court for permission to proceed with the lawsuit or the Chapter 13 debtor could offer to pay the debt back in his or her Chapter 13 Plan.  The debtor would then have an opportunity to object to this request and normally this happens if the plan provides for repayment.