AMS is a system for routing modulation around, for example using joystick +Y ('modwheel') to change cutoff or using Velocity to control an LFO speed, for example.
AMS mixers allow you to perform operations on different AMS, for example mixing two AMS together, or multiplying them together, quantizing them, etc.
I'd presume the 'lag' mode is either a kind of delay, or a glide like portamento when used on Pitch.
Current Gear: Kronos 61, RADIAS-R, Volca Bass, ESX-1, microKorg, MS2000B, R3, Kaossilator Pro +, MiniKP, AX3000B, nanoKontrol, nanoPad MK II,
Other Mfgrs: Moog Sub37, Roland Boutique JX03, Novation MiniNova, Akai APC40, MOTU MIDI TimePiece 2, ART Pro VLA, Focusrite Saffire Pro 40.
Past Gear: Korg Karma, TR61, Poly800, EA-1, ER-1, ES-1, Kawai K1, Novation ReMote37SL, Boss GT-6B
Software: NI Komplete 10 Ultimate, Arturia V Collection, Ableton Live 9. Apple OSX El Capitan on 15" MacBook Pro
X-Trade is right - AMS Lag is for smoothing or delaying modulation changes. This can be used to smoothly change one or more parameters in a program, but not for changing from one program to another.