First, why would you use a SE cable when the LCD-3s are inherently balanced and even come with a balanced cable, though of course there are lots of aftermarket balanced cables available as well?
Second, it isn't about watts into phones, it's about amp design. The TBI Millenia requires a resistor box to reduce the noise floor because it is a class-D chip amp designed to work only with speakers. By adding a resistor circuit in a separate box specialized for the headphones to be used, the amp's designer, Jan Plummer, has provided a relatively simple and inexpensive way to eliminate the audible noise for a number of different cans, including the LCD-3s and the HD-800s. He creates different circuit designs for SE vs. balanced setups, and they work. Repeat: with the resistor box there is no audible noise with this 32-wpc amp, and the total cost of the system is $600 delivered to the US. It is also tiny, so return shipping should be reasonable, particularly within the US, but perhaps even from Israel though I haven't checked those rates.
With the Cyclops feeding my LCDs via the stock balanced cables there is no audible noise even without a resistor box. None. Moreover, the power available is totally irrelevant as long as the volume is controllable, and it is easily controllable on this amp. I listen to everything from old rock recordings to jazz to classical to the Red Hot Chili Peppers and have no problems modulating the volume to fit the recording. Could I blow the headphone transducers if I crank it all the way? Yeah. Would it be really stupid to do that? Yeah.
The LCD-3s are rated for 12 wpc into 45 ohms. The Cyclops can put about 20 wpc into that resistance before clipping. This isn't that huge a difference, and for a large portion of the volume dial, the amp is not putting out anywhere near the cans' limit. At their limit, the LCDs are pumping out 120dBs, enough to deafen a person pretty quickly. If you are even reasonably careful, or not already deaf, this is just not a real problem.
I understand folks being cautious about this, because I was in the same boat a few months back. But after an e-mail exchange with Audeze, discussions with Jan Plummer of TBI and Klaus Bunge of Odyssey, plus some back and forth with the folks on the speaker amps thread, I took the plunge and did a comparison of speaker amps vs. the MJ and Soloist. I'm extremely happy that I did, because I found amps that I liked much better than the headamps, for very reasonable prices (the Millenia is an absolute bargain).
I recognize that speaker amps aren't the right solution for everybody, particularly for cans that don't have the power-handling capabilities of orthos like the LCDs. But if you have LCDs, and you want them to perform optimally, you need to at least consider a speaker amp: there are a lot more of them out there at all price ranges than there are headphone amps, because the audiophile speaker market is still so much larger than the market for high-end cans. Not all speaker amps work well with the LCD-3s (I didn't like the Emotiva Mini-X at all... but it's a $200 amp). However, I know at least 2 that do work well, at least for me.
My recommendation is not that everybody should just use speaker amps instead of head amps. It is that everybody using orthos, or even HD-800s, should open their minds to the possibility that there is a speaker amp out there that will meet their needs better than the headamps available and/or at a better price. In my view, LCD-3 owners owe it to themselves to at least consider, if not try, some of the available speaker amps.