Amp power needed is determined by the headphone's sensitivity in dB/mW. The goal is 110 dB, so to figure out how much power you need in mW use this equation: 10 ^ ((110 - sensitivity) / 10). The LCD-2F has a sensitivity of 93 dB/mW, so we do 10 ^ ((110 - 93) / 10) = 10 ^ 1.7 =
50.12 mW. You can replace 110 with any other dB goal, like 80 dB for a safe average volume level or something. It's also helpful to know that every 10 dB increase in volume, you multiply the power by 10 (so 20 dB is 100x, 30 dB is 1000x).
To figure out how much power you're going to get from an amp's voltage, you use the impedance. Power = Voltage ^ 2 / Impedance. The result is in whole Watts, so to get to mW you multiply by 1000. In the iDSD's 1.65 Vrms case and the LCD-2F's 70 ohm impedance, you do 1.65 ^ 2 / 70 = 0.03889 W * 1000 = 38.89 mW. You can then do the opposite of the first power equation I posted to find what that does to the volume, which would be 10 * log(power), or 10 * log(38.89) = 15.9 dB increase. Add that to the sensitivity of 93 dB/mW and you get 108.9 dB of volume.
Some headphones, like Sennheiser's, will list sensitivity in volts instead of mW. It's sort of a combination of the mW value and impedance. You can skip the voltage to power equation and just take a log to find the change from a voltage, but you do 20 times the log instead of 10.
That's a lot of math and everyone hates math.
This page has a calculator for both power and voltage changes to volume. Just enter the change in power/voltage or the change in dB and it'll calculate the other.
You can't always go by the amp's rated max output. If it has high output impedance or can only produce so much current, voltage output will decrease as the impedance decreases. An example of this is the O2, where the relatively low max current reduces the max voltage into low impedance loads (by design to reduce volume). The iFi should be OK for its max 1.65 Vrms at 70 ohms, the 1 ohm output impedance is negligible and it appears to have plenty of current (130 mW at 16 ohms requires 90 mA, 1.65 Vrms at 70 ohms only needs 23.5)
It's hard to say what gain setting you should use. The Eco mode will have plenty provided you can reach its 2 Vrms maximum, but I don't know how the gain is set up. If Eco is unity gain (1x) like I suspect it might be, you may be maxed out at 1 Vrms with a 1 volt source like your iPhone. But then 1 Vrms might be all you need with your listening habits. iFi seems to be suggesting volumes between 12 and 2 o'clock on their product page, so I think you're safe on Eco.
To be completely accurate, it's exactly 10 times the power per 10 dB, so 30 dB increase is 1000 mW. The extra 24 you got is because of a rounding error when doubling power every 3 dB; it's actually 1.995 times the power per 3 dB (10 ^ 3/10 = 1.995) but 2 is accurate enough when making small changes.
I'm being super nit-picky.