If you're talking about their "Realskies", this is 100% identical to going to https://hdrihaven.com/ and picking a skybox. They just ship it with the product, but it's still not animated. It is technically not impossible to play-back 360° HDRI videos of a sky, but it's challenging.
Yes Lumion Realskies is just a HDRI image, even they're very nicely integrated, maybe something to consider.
But their generated skies are quite nice too, which gives some advantages when it comes to animations.
I have used Lumion, but like Enscape a lot and I'm sure you're doing a big and good job to implement as many features as possible within the resources you have. Maybe just more variety to the clouds can do the trick? Like PowerTower said, the "repetitive shapes" of the clouds makes the sky look off compared to what's Enscape is capable of.