The new civs tech trees and bonuses are already kind of out there but if I had a say in it, I would have done something like this...
Tatars - Give them full Stable. Besides that, it would be kind of difficult to make them different from Persians.
Cumans - Two starting Scout Cavalry is a popular suggestion but would be super OP. What might not be OP is starting with a Horse unit besides Scouts and Villagers. It won't give Food, and is faster than a Llama, so it won't step on the Incas toes. It has less LoS and speed than a Scout and, most importantly, no attack. Another "Steppe-y" bonus would be Free Thumb Ring, which would make Cav Archers instantly viable in Castle (I think). Other than that, I got nothing off the top of my head. You don't see Cav Archers and, uh, Champions together very often.
Lithuanians - I can't come up with anything for them specifically, either, besides "fully upgraded Paladin and Hussar." The Polish-Lithuania Commonwealth exported tons of their surplus grain, so a Farming bonus? They were the last Pagan state in Europe, so...resistance to conversion? No civ gets fully upgraded Paladin and Siege Onager; Celts miss Bloodlines and Plate Barding, Teutons miss Husbandry. Anyway, my ideas for these guys are really starting to sound like Teutons.
Bulgarians - So combining their propensity for copying Byzantine tech with Steppe warfare, you can kind of do whatever you want with guys and it won't really be a stretch. There are some bonuses I want to see that aren't characteristic of the Bulgars but wouldn't be out of place, either. Not necessarily saying these should be all their bonuses.
50% faster moving Scorpions is a rip off of the Mongol UT, but at least this would be available for free from the Castle Age onwards. I think this would make Scorpions viable in Castle and on, and the Bulgarians definitely copied Byzantine Ballista tech.
Siege Tower holds 2x dudes. The Bulgarians used Siege Towers, and the Avars (who aren't the Bulgars but whatever) also used humongous Siege Towers on Constantinople. A regular Siege Tower can reach 1.2 tiles per second speed and a Mongol Siege Tower can reach speeds of 1.7 tps. This hypothetical Bulgar Siege Tower can hit 1.8 tps. It'd be hilarious to watch, and would be useful for moving Halbs and Champs around.
Champions +3 Armor. So like, two Champions can't beat one Paladin. With this bonus, two Champs would barely scrape by a Pala.
Hussars +2 Pierce Armor. You could probably remove Elite Skirmisher so that this civ would have only 1, anti-Archer trash unit, and would have a harder time vs Pikemen in trash wars. Anyway, these Hussars would wreck Arbalests, and might do well vs Cav Archers.
[This message has been edited by The Battler (edited 10-12-2019 @ 10:43 PM).]