I have updated the guide to the lakes in Mt. Rainier NP, with a description, map, and a list of the lakes. The guide focuses on those which are recognized with names on USGS or NPS maps or a commonly known, named and located.
That said, there are currently 400 mapped lakes in Mt. Rainier NP, but less than 50 have official names listed on maps for the NP. Many of unnamed lakes are either small, remote or intermittent (seasonal or temporary) and haven't required a full identification or description in publications or on maps.
The lakes in Mt. Rainier NP are divided into three catagories, two major ones and one obvious one. The first to two types of lakes are divided by their location, namely elevation, in relation to the treeline, where they are either surrounded by forests or above the treeline and are open or in geologic features such as tarns, cirques, etc. The third type are the scenic or photogenic ones, most of which are alongside roads, listed below for easier identification for location.
Unfortunately there isn't much on-line or published information about the lakes in Mt. Rainier NP, and what does exist are often research studies related to water resources investigations or academic research. The Washington State Department has some information with their Water-Supply Bulletin series on lakes. The USGS did one study, WRI 84254, in August 1983, available here, on a dozen lakes.
The description Web page on the lakes has photography tips for the lakes in the NP.