NDWI Calculation for Landsat Images from 1985 to present

I am studying water changes on lakes and I am need to calculate the NDWI for my control lake in 1987, 2000 , 2011, 2015, 2017 and 2019. I will be suing the Amazon Open Data Program to store and process my images and to calculate the NDWI.

I know that the latest Sentinel -2 calculates NDWI for images but I need to develop a methodology using Landsat and Sentinel in order to estimate Water area reduction for lakes around the world.

Any Ideas of where to start…

There is currently no Landsat data prior to 2013 on AWS. They should come in the mid-term period, but no precise ETA was yet stated.
GCP has Landsat-5 data, full archive.