Are there any canon works that tell what Lando Calrissian has been doing during the events of TFA and TLJ? Is he involved in New Republic politics or in the New Republic fleet? Or has he gone back to gambling?
As of now, it remains currently unknown.
From Lando Calrissian's wookieepedia page, it does state that after the battle of Endor, Lando participated in the Battle of Naboo and ended an uprising in the Anoat system and in Bespin itself during the Battle of Jakku.
Although Lando does not make any appearances and isn't even mentioned in the two released sequel trilogy films, The Force Awakens and The Last Jedi, he is mentioned briefly in the canon novel, Bloodline by Claudia Gray (which takes place six years prior to The Force Awakens). In the novel, Lando is mentioned among Leia's list of friends and allies that supported her after her true parentage was revealed in the Senate:
Star Wars: Bloodline by Claudia Gray, p 294 - 295
Tai-Lin had come through for her, and despite Varish's awkwardness, she had defended Leia from the start. Greer and even the young Joph Seastriker had come around within a day or two; a handful of others were likely to follow. A few people from her past, including Ackbar, Nien Nunb, and Lando, had messaged or sent holos that showed their compassion and loyalty.
There are no current published comics or novels that focus solely on an older Lando as of yet and it remains to be seen if the character will have a supporting role or even a cameo within the final sequel installment, the upcoming Episode IX and nothing has been confirmed. However, Lawerence Kasdan, one of the writers for The Force Awakens had stated shortly before the first film's release around 2015:
"Right now, there’s no Lando Calrissian in this movie. But Lando I don’t think is finished in any way, shape or form."
It remains to be seen if this is in regards to the sequel trilogy films or just within the Star Wars universe in general.
So far within the overall Star Wars universe, the character of Lando Calrissian has appeared on the television show, Rebels in the episode, Idiot's Array (which takes place several years before Episode IV: A New Hope) and will appear in the upcoming film, Solo: A Star Wars Story which is scheduled for release in May 2018; this time portrayed by Donald Glover. This movie, as well, will take place before Episode IV. Back in 2015, a five part comic miniseries called Lando was published as well and takes place before The Empire Strikes Back. Apart from being mentioned in Bloodline, he does have a role within the novel, Aftermath: Empire's End which takes place shortly after Return of the Jedi.
But as for the sequel trilogy, we do not know if Lando is involved in the New Republic's politics or fleet, gambling, the Resistance, or if he still resides in Cloud City throughout the events from The Force Awakens to Episode IX. We'll have to wait for more novels, comics, and quite possibly, Episode IX itself to either mention or inform us of Lando's whereabouts.
As of July 2018, LucasFilm has confirmed that Lando Calrissian will be appearing in Star Wars: Episode IX with Billy Dee Williams reprising his role alongside fellow Star Wars veteran actors, Mark Hamill, Anthony Daniels, and the late Carrie Fisher.
Joining the cast of Episode IX are Naomi Ackie, Richard E. Grant, and Keri Russell, who will be joined by veteran Star Wars actors Mark Hamill, Anthony Daniels, and Billy Dee Williams, who will reprise his role as Lando Calrissian. The role of Leia Organa will once again be played by Carrie Fisher, using previously unreleased footage shot for Star Wars: The Force Awakens.