Niantic have announced a few changes to Pokemon GO's Research Breakthrough rewards and Eggs for the following weeks, and they wrote that Lugia, Ho-Oh, Latias and Latios are coming as Research Breakthrough encounters as of 01 May 2019.
The exact timing is 01 May 2019, 1pm PDT / GTM -7, and the Research Breakthroughs will last until the end of June 2019, so you've got two months worth of potential encounters.
Basically, completing seven days worth of Field Research grants you a Research Breakthrough, which earns you an encounter with Ho-Oh, Lugia, Latios or Latias.
Note that even though you can binge Field Research tasks as much as you'd like, it's only the first Photo Disc spin of the day that grants you stamps, seven of which are needed for the Breakthrough.
At the same time, this means that the likes of Suicune, Entei, Raikou, Regice, Registeel and Regirock are out the door come May.
As for Eggs, Niantic wrote that different Pokemon will hatch from Eggs as of 26 April 2019, at 1pm PDT / GMT -7.
Turtwig, Chimchar, Piplup, Bonsly, "and many more" will be hatching from 2km Eggs.
Cubone, Combee, Buizel, Glameow, Bronzor, Skorupi, Croagunk and others will hatch from 5km eggs, which 10km ones will hatch Mawile, Absol, Shinx, Cranidos, Shieldon, Riolu and more.
"If you're lucky, you may encounter Shiny Meltan when you open the Mystery Box from Wednesday, April 24, at 1:00pm PDT, until Sunday, May 5, at 1:00 pm PDT", but Mystery Boxes require you to send a Gen 1 Pokemon from GO to Pokemon: Let's Go Eevee/Pikachu on the Switch.