No, I don't think the Lehmann Black Cube Linear qualifies, even though it's quite good. I happen to have one, it was one of the first amps I got back in 2005 and I still have it.
I think the Zana Deux is definitely better, and maybe a Corda Symphony. I recently got a balanced Beta 22, but I don't have a balanced HD800 cable yet so haven't tried it with the HD800.
I understand budget is limited (whose isn't?) and you're looking for a good value (like everyone else). It can be annoying when people recommend expensive amps. But the HD800 is a good headphone precisely because it is sensitive to upstream components, and improves when those components are better.
It's not easy to make a good recommendation without knowing how much experience you have and what your perspective is on the differences between the amps we're talking about. If I went out on the street and just grabbed the first five passersby, I would bet that all five would say the difference between the ZD and Lehmann BCL is very small, maybe even indistinguishable. But for me, and some other crazy people in this thread, the differences can seem quite large. When one becomes accustomed to a specific sound, and then make a small change, the change can seem very large. It could be something like just a tiny bit more upper bass quantity, so drums sound just a little bit fuller-bodied.
Having said all that, I think one can be quite happy with a HD800 > Lehmann BCL > Lavry DA10 system. If I had to make a change here, I would improve the source. Yes, Team Source First people are especially crazy.
Feed the BCL as good a signal as possible, and it'll do a decent job. You can even drop the HD800 for an HD650 or HD600 instead. I know this is an HD800 thread, but someone has to say it.