Your understanding is correct. The first step is to contact the attorneys for, or the property management company, and ask them to provide a partial release of lien. The title company may be willing to do this on your behalf. Often times, judgment creditors will try to use the judgment as leverage to negotiate a settlement. You could settle or not, as you wish, but you are not required to pay anything to the judgment creditor in order to get the partial release.
If they won't cooperate, there is a different procedure under the Property Code, as outlined by one of the other answers here, that allows you to release the lien after giving the judgment creditor a 30 day demand to release the lien. It's not difficult, but you have to follow the process exactly, so it's best to have an attorney do it for you.
Finally, you can also pay the judgment lien "under protest" so that you can go forward with closing and then sue later to recover the money.
I am licensed only in Texas. Offering information of a general nature in response to a question is not intended to be legal advice in your state.
There was a Texas case in the early 90's that held a judgment creditor can be held liable for clouding title on your homestead and refusing to release the lien. (Tarrant Bank vs. Miller). Realistically however, you need to close quickly and probably do not want to file a lawsuit and prove that they caused you damage so perhaps you can consider a certified demand letter to release the lien pursuant to Tarrant Bank v. Miller.
Another option is to file your own partial release of the judgment pursuant to a new provision in the Texas Property Code. Ask your title company if they are ok with a partial release as it relates to the homestead. This procedure is done under Texas Property Code Section 52.0012. This procedure has to be done correctly, you may want to consider hiring a judgment defense attorney.
My comments are not legal advice and are for informational purposes only.