In recent years, our cavity coupled ultra-cold Rb87 cloud experiment was used to investigate the Dicke phase transition in a 2D checkerboard lattice. In a next step, an optical lattice potential in the third dimension is being added, which increases the requirements on the stability of the probe laser and creates the need for a stabilization tool of the lattice laser. A new type of carbon-fiber based transfer cavity with active temperature stabilization, high mechanical stability and low thermal expansion used for the Pound-Drever-Hall laser lock of the probe laser is presented. By using the low coefficient of thermal expansion of unidirectional carbon fiber tubes and by suppressing the thermal expansion of aluminum and glues used in the cavity assembly along the optical axis of the cavity, a very low coefficient of thermal expansion of 1.7x10^(-6) per Kelvin of the assembled cavity was reached. The remaining coefficient of thermal expansion was used to tune the cavity resonance by heating and convection cooling. Using a Toptica DLpro 780 diode laser, the cavity was locked to a wavemeter as an absolute frequency reference with a very slow feedback loop to the cavity heater reacting on a timescale of minutes. As a result of this very slow reference lock, the transfer cavity locked probe laser showed stable single mode operation over the course of several weeks of operation. A standard deviation of 1.8 MHz from the set point wavelength was observed in a 16 h measurement, while frequency deviations stayed below 10 MHz at all times. The transfer cavity with a Finesse of 2x10^3 and a linewidth of 4x10^2 kHz was used to narrow down the relative linewidth of the probe laser to a few tens of kilohertz. The design presented was also used in a second cavity to stabilize the lattice laser and to consequently reduce heating of the atoms.