The HA API is not made for low latency updates. In case you have network lights which are directly supported by Hyperion, always go via the non HA route.
For your lights you might need to check where the latency comes from. Given you are not sharing too much details, it is hard to say.
Latency could happen as Hyperion does requests via a bad Wi-Fi connection.
To sort this out you could enable Debug logging in Hyperion.
There you will then see how long one API request to HA takes.
In case, you issue is more that you do not see frequent updates, you might want to test if reducing the latch time helps.
You should enable expert settings to see the element. You should not reduce the latchtime below the API request time (you checked above). Also include some buffer.
Hoping that this provided you with some pointers.
As every setup is different you need to explored the influencing dimensions.