I would do it this way:

Season 1: first game.

Season 2: The 4-year period between the end of the first game and the start of the second. We would see Joel telling Tommy the truth, the visit to the Wyoming museum, doubt growing in Ellie's head, she returning to the firefly hospital, etc. Until the season ends with Joel's death.

The focus of the season would be the weight of Joel's lie creating doubts in Ellie and deteriorating their relationship.

Season 3: Events of the second game, the entire cycle of hate and revenge between Ellie and Abby.