The length of time liens remain in effect is defined under state law. So I would recommend going online to search for state law and looking at what it says about mechanics liens. Most states post state laws on the state's own website, so this shouldn't be too hard to find.
However, since the company that placed the lien can't find it, I would suggest that you settle with them & ask them to sign a release of the lien in exchange for some cash to call the matter resolved. Whether the company can find the lien in their records is immaterial, because the county records will control whether you have the right to sell or refinance your property. Get an experienced real estate attorney to take care of this for you!
Hope this perspective helps!
Yes, they can expire. Texas Property Code Section 53.157 sets forth the specifics of the discharge of a mechanic's, contractor's or materialman's lien. It provides that if suit to foreclose the lien is not timely filed, in the county in which the real property affected by the lien is located, the lien may be discharged. There are time frames for the suit filing deadline in, among other provisions, Sections 53.158, 53.175 and 53.208 of the Texas Property Code. Look to see which provision best fits your situation.