Is there any statutory/case law to support the position that the State does not have to pay fees/costs for the filing of a lis pendens relating to the forfeiture of real property under CCP Art. 59.04(g)?

Or is the State treated like any other litigant and required to pay the clerk upon filing?

At first blush, the answer would appear to be "yes" to your first inquiry. Section 154.004(b) of the Local Government Code provides:

If a county officer is paid an annual salary, the state or any county may not pay a fee or commission to the officer for the performance of a service by the officer.

However, in comparing the legislative history behind section 154.004 and section 118.011 (the recordation fee schedule for county clerks), the attorney general concluded that the state is not excused from paying real property recording fees, at least insofar as the Railroad Commission is concerned. See Op. Tex. Att'y Gen. No. DM-360 (1995). Opinion DM-360, while directed to the Railroad Commission and an inquiry about filing documents concerning the plugging of wells, couched its conclusions broadly in terms of the "the state" and its liability for filing fees in real property recording matters. With that said, the attorney general's opinion is just that; an attorney general opinion. It's not a holding of a court of competent jurisdiction. So, I suppose the answer must be, in the inimitable words of the soothsaying Magic 8 Ball, "Signs point to No," but it might be argued otherwise.

As to whether the state generally is liable for costs in civil cases, the answer is "yes." See Tex. Loc. Gov't Code sec. 154.004(d)(2).