The shutdown date will be Saturday, April 27th, 2019.
Friday April 26th, 2019 will be the last day of service.
Gothamist reports that the MTA has confirmed this information:
The MTA has confirmed that the final day of L train service ahead of the shutdown will be Friday, April 26, 2019. Ahead of that disruption, the authority will also be rolling out three “mobile information centers” to meet with customers and help them plan their routes.
Riders will also get a taste of the future misery to come in the form of partial L train shutdowns during eight upcoming weekends. According to the MTA, L train service will not run between Eighth Avenue in Manhattan and Broadway Junction in Brooklyn on the weekends of: February 2-3, February 9-10, February 16-17, February 23-24, March 2-3, March 9-10, March 16-17, and April 27th and 28th.