Checking if a lecturer can be heard clearly from the back of a room
There's possibly an easy way out: Add two mics, one near the speaker and one in the back of the room. Run both signals through speech recognition software. If there is textual output from both and they agree, then the voice must be loud and clear. The software must be able to handle the language spoken though.

Other than that, there is research and standards on speech intelligibility. Perhaps it is better to start with a simplified model of intelligibility. Two important factors are speech level and noise level. By carrying out preliminary listening tests and measurements in the space, you can determine what the baseline noise level ($N_0$ dB) in the back is and how loud the speech must be ($S_0$ dB) in the minimum at the front mic for it to be intelligible in the back. Then during a lecture, you would detect voiced segments of the audio with the front mic and measure the speech level ($S$ dB) at the front during voiced segments and noise level ($N$ dB) in the back during non-voiced segments. If $S-N \ge S_0-N_0$, the speech should be intelligible. When measuring levels, you should weight the spectrum (by running the signal through a filter) so that level best reflects speech intelligibility or the detrimental quality of the noise. You would need to look into voiced/non-voiced detection, or simply have a threshold level for $S$ above which you classify the input as voiced.