The non-wired screenshot:


Yeah, I inserted the pumps via-paint.

The wired screenshot:

So now we have all the structure, let's start.

We activate the first lever we want to get the liquid from:

• Orange: Honey.
  
• Red: Lava.
  
• Blue: Water.

Each color lever is connected to the input pump of its correspondent fluid.

Then we activate the second lever to mix both liquids.

• Lava + Water = Obsidian.
  
• Lava + Honey = Crispy honey block.
  
• Water + Honey = Honey block.

The exceding of the second liquid will fall into the hole with another input pump at the right, which is activated by the "remove excess" lever, and connected to an output pump in the underground, in a very large cavern, which will stash our remaining liquids forever... I hope.

This is basically how this works.

When your reserves start to get empty, go to the refill lever and press it. It will activate 3 timers that activate each liquid's pumps to multiplicate it and get your reserves back.
I added a green torch that says the refill is working, and a red torch that says it's not.

For the refill's start you have to wait a while, it seems like it's working at the start, but it's not, just moving the fluid. Also having a quite big ammount of liquid helps.
Anyway you can start it and do something else while it works!

So there you go. Have fun getting mixed liquid blocks!

If I misspelled something let me know it and I'll fix it as soon as possible.
Thanks for reading.