Robert, Robert, you'd think an aspiring attorney would see a few loopholes in that statute :)  First, I agree that threatening something you can't legally do is folly.  But as to the statute, stick with me for a minute:

in furtherance of any improvement  YOU ONLY UNDERLINED "OF ANY IMPROVEMENT".  CERTAINLY A TITLE SEARCH IS NOT A PHYSICAL IMPROVEMENT BY ANY STANDARDS, BUT AREN'T ALOT OF REFINANCES FOR HOME IMPROVEMENT??  A TITLE SEARCH COULD ARGUEABLY BE WORK IN "FURTHERANCE" OF AN IMPROVEMENT.

or the owner's, part owner's, or lessee's authorized agent, YOU UNDLERLINED IT BUT SKIPPED IT IN YOUR ANALYSIS.  HERE IN SC, BEING AN ATTORNEY ONLY STATE, WE DO SIGNIFICANT WORK FOR ATTORNEYS.  SO, IT WOULD BE MY HUMBLY, NON-LAW SCHOOL GRADUATE, OPINION THAT IF IT CAN BE PROVEN IN COURT THAT THE "OWNER" HIRED THEIR OWN ATTORNEY, THEN THAT PERSON IS DE FACTO THEIR "AUTHORIZED AGENT".

So as far as I can see, by your Ohio statute, IF one could prove that the title search was done to obtain monies in the construction of a new home or the improvement of an existing home AND IF it can be proven that the owner hired the attorney who authorized the work, then a filing of a mechanic's lien would prevail.

How would you feel if someone you had no contact with at all filed a lien against you? 

Finally, I would be livid! but I would be on the phone finding out why I have a lien on my home for something I paid for at closing.  Surveyors and Contractors file mechanic's liens all the time.  Many times before the statute of limitations is even up for the filing, the property has been sold to new owners.  The mechanic's lien still applies but do you honestly think the plaintiff cares one whit about the new owners--they want the money they are entitled to.

Just my thoughts!