Engineering very high impedance resonator with coplanar waveguides
I have read that a coplanar waveguide (CPWG) acts as a lumped LC oscillator circuit, 


This isn't particular to coplanar waveguide. Any kind of transmission line is characterized by a an inductance and a capacitance per unit length. 

The line only act as a lumped resonator with the given capacitance and inductance if the line is exactly 1 unit of length line (for example, if the specified capacitance is 1 pF/cm, and the length is 1 cm, then the capacitance will be 1 pF), and if the operating frequency is low enough for this length to be "short" (meaning the wavelength is 10x or more the line length).


  and its impedance is usually set around 50 ~ 100 Ω.


I think you are talking about the characteristic impedance here, which is the ratio of the voltage and current signal amplitudes associated with a travelling wave on the transmission line. 

The characteristic impedance is not at all the same as the equivalent impedance of a given structure (for example an open or shorted stub line) constructed from the transmission line.


  The reason why I am asking this is that there are potential applications for the resonators with very high impedance values (say, larger than 10 kΩ),


It's generally not practical to make transmission lines with characteristic impedance too far outside the 10 - 400 ohm range. 

But we can make a resonator using a transmission line, and the input impedance is not limited by the characteristic impedance of the structure. 

You can google "coplanar waveguide resonator" or "microstrip resonator" or "coaxial resonator" to get numerous examples of ways to construct such resonators.