For anyone still looking, acceleration is replicated to simulated proxies in ALyraCharacter with the ReplicatedAcceleration struct.
They calculate the acceleration value inside the overridden PreReplication function and compress it. Then it is decompressed in the OnRep_ReplicatedAcceleration function. From there, the replicated value is sent to the LyraMovementComponent via the SetReplicatedAcceleration function where it will override the default acceleration value that the movement component returns. They also override SimulateMovement in the movement component to ensure that the replicated value isn’t overridden by the default acceleration value.
At least that is what I made of it. 
. Implementing this into my current setup allowed my pivot anims to replicate to simulated proxies. Without it the pivots would only play locally