What's the minimum amount of energy needed to remove CO2 from the atmosphere?
The OP is specifically interested in the efficiency of removing $\ce{CO_2}$ from ambient air, rather than from point sources like power plants.  The former is obviously less efficient because the $\ce{CO_2}$ is far less concentrated.
According to p. 50 of the the SAPEA* Evidence Review Report No. 2
(Schlögl, Robert, et al. Novel carbon capture and utilisation technologies: research and climate aspects. 2018.  Available at : https://www.sapea.info/wp-content/uploads/CCU-report-proof3-for-23-May.pdf),
&quot;the thermodynamic minimum energy required to extract CO2 from ambient air is about 250 kWh/(ton $\ce{CO_2}$).&quot;  This equals 0.99 MJ/(kg $\ce{CO_2}$).
The OP asks that we assume the $\ce{CO_2}$ came from a coal-fired plant that produces 24 MJ/(kg $\ce{CO_2}$).
Hence (assuming SAPEA's number, and the OP's, are correct), at at the theoretical maximum thermodynamic efficiency, the energetic cost of capturing $\ce{CO_2}$ from ambient air is 0.99/24 x 100 = 4% of the cost of the energy generated in producing that $\ce{CO_2}$ from a coal-fired plant.
Of course, this is not a lifecycle analysis.  One needs not only to determine the actual thermodynamic efficiency of the process, one also needs to account for the energetic costs of putting the infrastructure in place for the carbon capture, and for maintaining that infrastructure.
*For more information on SAPEA, see:
https://en.wikipedia.org/wiki/All_European_Academies