LB assault trades the aim assist from SD thermal with range (boosting bullet accuracy), both have good target clarity.
Counterbalance makes your recoil vertical (smooth 12:00, see spoiler) but rodeo tightens your shot grouping, albeit a very mild affect. (Information gathered after watching some YouTube videos with enough replay and squinting)
Counterbalance is necessary for high fire-rate weapons and controlling fast successive bursts (Arminius, Doctrine, Bullet Piss of Malok, Hawksaw) but since Lyudmila is the low fire rate archetype, rodeo may be a better choice when controlling the four bullets in a single burst and repeat.
Hand-laid stock is perfect for the Lyudmila just so that it works within its archetype. (a lot of range by default, but it can't be used due to lack of stability)
I picked the rodeo roll because I had one like this before the update, but used as infusion material when the Arminius God roll came. Old Lyudmila just had Hand-laid stock as it's lone stability perk and its bursts were controllable. I know rodeo will be an improvement.
[spoiler]To use headseeker on this gun on a guardian, aim for their breast below the shoulder on your right to compensate for recoil pattern (smooth 11:00)[/spoiler]
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I was curious on what Rodeo does, I got many weapons with it recently