I represent an insurance company that has a lien for medical bills on a personal injury case. Can the opposing counsel pay the settlement proceeds to the client and tell the client it is their responsibility to pay the lien without consequences to counsel?

To answer the question, one would have to know the type of lien. There are some liens that statutorily require counsel to maintain the funds until the lien is resolved. Other liens are created by contracts, such as in a policy of insurance. If an insurance carrier paid out first-party or medical benefits, then usually in the insurance contract there would be a lien created and the insured would have to pay the money back out of any third-party settlement or judgment.