There was apparently nothing specific as a line item listed on the Somervell County Hospital District agenda for January 31, 2019 to indicate that Somervell County Hospital District had not paid state taxes. Also no line item agenda or indication from the Somervell County Hospital District agenda for Dec 27 2018. Nor from the November 29, 2018 meeting.
The lien was filed by Texas Workforce Commission against Somervell County Hospital District/Glen Rose Medical Center. According to the TWC, they would have notified Somervell County Hospital District in advance to allow for time to pay the taxes (most likely unemployment tax, although the letter of notification with more specificity ought to be available through a Texas Public Information Request)

What is a state of Texas tax lien and why?
State Taxation Law
Sec. 113.002. TAX LIEN NOTICE. (a) The comptroller shall issue and file a tax lien notice required by this chapter.
(b) A tax lien notice must include the following information:
(1) the name and address of the taxpayer;
(2) the type of tax that is owing;
(3) each period for which the tax is claimed to be delinquent; and
(4) the amount of tax only due for each period, excluding the amount of any penalty, interest, or other charge.
(c) A tax lien notice may include other relevant information that the comptroller considers proper.
Acts 1981, 67th Leg., p. 1518, ch. 389, Sec. 1, eff. Jan. 1, 1982.