In case you find so much to critique in a published article, book, or paper of your current university lecturer or professor, how prudent is it to review it, and how do you go about it?
Critiquing research help to further academic discourse. It is the norm in the academic world. I have seen a lot of critiques to published articles: both articles are normally published in the same journal and the original author is given a chance to respond. Unfortunately in Ghana, most professors and Snr lecturers carry a big ego. Some might take it wrongly as 'a student challenging him intellectually'. I believe you can critique it but you should be mindful of how you go about it. You can set up a meeting with him and point out what you think about the research. Discuss both the positive and negative and allow him to defend him stance
This looks like conflict of interest. If you can be objective enough then you may go ahead. But if you cannot be objective, do not accept to review it. Better still you may do that without fear or favor. Reviewing builds your academic credentials.