Referring to previous literature review How valid is to refer to previous literature reviews in other papers to 'create' a thorough review? 

The thing is that I am working in a new methodology, which I will compare with the current state-of-the-art (published in 2017). In there, the authors have done some literature review, which is not thorough. Hence, I want to focus only on the work that they didnt cover. In addition, there is older work what has been reviewed by others. Putting my literature review contribution, together with the paper from 2017, and together with the two oldest papers, then we have a 'thorough' review. Is this a valid approach?
I would suggest that you include the work you have read, as well as the works that the other papers mention. The purpose of the literature review in a paper is to describe related pieces of work, and showcase how your work complements, surpasses and stands out. This strengthens the narrative of your research and helps the reader understand what makes your paper valuable, compared to other approaches. In order to achieve that and build a more complete image, you need to include as many related papers as you can find and study in the literature review part.