It depends

You can view this as an assignment that you assigned your contract rights with the company 1 who owes you, to the company 2, whom you went to the lawsuit with. The contract rights under concern are between you and company 1. If several years ago at the lawsuit you assigned this right to collect to company 2 and so notified compnay 1, then you have no obligation whatsoever to company 2, and they are responsible for the collection. If it runs out of Statute of Limitation, it is company 2's problem, not yours. Your lawyer is wrong.

However, there are some requirements to make the assignment valide. First, since the assignment is designed for security, if it is over $5000, it must be in writing to satisfy Statute of Fraud. Second, it must be communicated to company 2.

On the other hand, your message is not clear how and when this assignment happened. You said, after losing the lawsuit, you padi restitution to company 2. Was this debt collection also a part of the settlement, which you assigned this debt company 1 owes you to company 2 as part of the settlement under the lawsuit? If so, then it is also a delegation that you delegated company 1 to pay the debt to company 2. In that case, if company 1 did not pay, you remain liable, unless it was a novation, that is, company 1 manifested intent to pay the debt to company 2 and release your responsibility. If this is the case, then your lawyer would have been right that unless you can prove company 2 did not use their good faith effort to collect, you must pay them. You have to check with your lawyer to see whether Statute of Limitation applies to the action arsing from the contract between you and company 2. I assume it does not so that your lawyer urged you to settle.