Luvoir is expected to launch in the mid-2030s. It is one of at least two exoplanet detection-and-characterization missions that is under study by NASA.
For others who are not familiar with the NASA studies, "expected" is probably too strong a word and "proposed" is probably more accurate. LUVOIR is one of four flagship mission concepts which NASA has provided with seed money. They will all be evaluated during the coming 2020 Decadal Survey of Astronomy and Astrophysics. The recommendations from that survey will then be used as guidance for NASA. So if the Decadal Survey ranks LUVOIR as a top priority (the missions are all so large that it is unlikely more than one would be funded), and if they meet their proposed timeline, then it would launch in the mid-2030s. So it's not yet a given that LUVOIR will happen (another mission could be more highly ranked), and the timeline should be taken with a grain of salt.
In fact, given the timeline, I’d be surprised if either Luvoir or HabEx, as currently envisioned, actually flies. There is a lot of technical innovation that will happen between now and then, even if the Decadal recommends one or the other.
(I work on yield modeling for the study. I make plots and animations of observations, and the times on the plot labels have disconcertingly-far-off times like 2036.)
It all depends on jwst. If that flops, or even if it only goes as planned, without the spectacular over-performance expected of nasa stuff these days, future large space telescopes will be shelved for a generation
At least the optical ones.
My worry is that jwst will be too short-lived. It cannot become the fixture for decades that hubble has been.
I imagine that an image of a planet around another star would have similar global impact as the Earth-rise picture from the Apollo missions did / does - sort of uniting people from different nations by giving them a visceral reaction from a totally new pov.