Despite the howls of anguish from SnyderBros worldwide, the DCU is kicking into a higher gear now with Lanterns, Supergirl, and Clayface all making it to various screens this year, and Superman sequel/not-sequel Man Of Tomorrow in pre-production right now, preparing to shoot shortly.
It looks like Lanterns will take place, chronologically, after Superman and before Man Of Tomorrow in the DCU, as news has now dropped that Aaron Pierre will appear in Man Of Tomorrow. These reports come from The InSneider and are confirmed by The Hollywood Reporter.

Pierre plays Green Lantern John Stewart in the HBO series. So, something will happen in Lanterns that sees John Stewart involved in shenanigans involving Brainiac?
David Corenswet returns as Superman, with Nicholas Hoult as Lex Luthor. All the rumors so far have stated that the two will be forced into an uneasy alliance to fight the technological alien threat of Brainiac (Lars Eidinger). Rachel Brosnahan (Lois Lane), Skyler Gisondo (Jimmy Olsen), Sara Sampaio (Eve Teschmacher), Isabela Merced (Hawkgirl), and Frank Grillo (Rick Flag Sr.) also return.
James Gunn wrote the script and directs again, with filming in Atlanta starting within the next few weeks.