I own L250's. I ran them with the twin Sumo subs for a while. L250's do not lack LF output at all. The main benefit of using the B380 with the L250's, or any other speaker for that matter, is the ability to dial in LF punch for low-level listening. Since you have complete control via the crossover gain and MX800 gains, you can ramp up the B380's output while your L250's are barely idling along. It is a real leap in system ability. Very easy to match the levels with the twist of the gain knob(s). You are in for a real treat.
I had forgot to mention that the MX800 is a good choice. Rare amp. I am still amazed that the big M series amps can still be had for less than $1k. I'd put any of my big M's up against the current high dollar offerings. HQ-SQ.
I want to clarify the connection of the crossover/MX800. The normal (non-inverted) RCA's path dictates the POSITIVE speaker/Sub connection. That means that if you connect the normal (non-inverted signal) crossover output to the the Right MX800 input, then MX800's Right Channel Speaker output POSITIVE is then connected to the B380's POSITIVE input terminal. You must keep the polarity correct wrt to the L250's because if you get it backwards, you will have cancellation, and no bass at all.
So..., if you hook it all up and the bass is almost non-existant, swap the polarity of the B380, it might be out of phase with the L250's.