Ayy thank you @pointyhatspointyears for the question! I don't know that I've fully elaborated on this before: they actually both got into liondancing before they set off as adventurers, so it's a bit the other way around! Lion dancing gave them the skills (and confidence, and conditioning) to pick up combat classes with relative ease.
Long answer under the cut!
A longer answer is that lion dancing slotted early enough into their lives (separately)! There's some variance as to how early they started:
Vira started around 5-7 years old, here's a fic based on their growth as a lion dancer! Before they became an adventurer, Vira was adopted by a Twin Adders dragoon named Izola, and they learned how to fight against a lance in close quarters.
Burakh, on the other hand, was taken into a rough situation as an infant. He had to break out first, around the age of 13 or 14, then recover from that situation, before he even grew the confidence to lion dance. His current fathers were called to find him; they reported that they did not find a girl, but announced to their estate that they found a son.
According to this interview with Khuan Loke Dragon and Lion Dance Association, it takes about 10 years of consecutive practice to gain the confidence/ability to do the acrobatic poles. The kids are really cute! The part I liked best is that they say, "you can't go on the poles if you have fear. You have to get rid of the fear first."
EVEN LONGER ANSWER BELOW: inspirations for Burakh and Vira's fighting styles!
Vira is a "street" fighter, who despite their Maelstrom training, got used to doing their own thing in close quarters. They've discovered that their bulk and size makes for powerful strikes when needed: it's more of a mindset than a "style", because they like sparring and jabbing around, but when things get serious, they'll put full weight behind their movements. They leverage their weight like in this vid, around 3.19!
Their main Jobs are Monk, Warrior, and Dark Knight.
Burakh's style of fighting is inspired by a blend of Silat Suffian Beladiri and Wing Chun (shown in the previous vid). Sometimes, the ideas behind both styles can contradict: for example, Wing Chun doesn't favor kicking, but Silat uses the whole body to exploit an advantage. He actually learned some moves from his fathers, before he found the confidence to join the nearby lion dance association. I really like how instructor Maul Mornie talks about the idea behind certain moves, the art style's history, and how that is applied in its forms. Silat Suffian Beladiri specifically uses the same or similar movements for weapons and non-weapon combat, so it transitions well into Burakh starting with Dark Knight/Samurai and leveling every class after. In my head he's a polyglot and someone who loves to travel to listen to the stories he finds, so the learning of new fighting styles intrigues him!
To come back into lion dancing, I thought it would be cool if no one in Eorzea knew that at any Heavensturn, it's possible a performing troupe would have both the Warrior of Light (Vira) and Warrior of Darkness (Burakh) performing for them! It's a little reprieve from the heroic life, but a purposeful one.