Short answer: Potentially February or March of 2020.
While it's not clear when recently released films such as The Lion King (2019) will be coming to Disney+, we know for a fact that company is at least open to adding their latest films to that service 200 to 249 days after its theatrical release, as seen in the chart below:
Number of Days Until it Was
Released on Disney+
|Captain Marvel||March 8, 2019||249 (8.3 months)|
|Dumbo||March 29, 2019||228 (7.6 months)|
|Avengers: Endgame||April 26, 2016||200 (6.6 months)|
Since The Lion King (2019) was released in theaters on July 19, 2019, it could potentially be coming to Disney+ sometime between February 19, 2020 to March 24, 2020.
Updated answer (January 28, 2020): Disney+ has added The Lion King (2019) to their streaming service on January 28, 2020.