You see.... the LC-1 takes a series of INDEPENDENT measurements. Usually at about 200Hz. That's a new completely independent measurement every 5ms or less. And there is no bleed-over from one sample to the next. It is, therefore ,IMPOSSIBLE to get traces like that unless the LC-1 is placed much further from the engine than the ALM and NB sensors.
Unless you are saying that the LC-1 is storing about 10-15 samples in a delay buffer and spitting them out FIFO style ( which is doesn't )... this just physically can't ( doesn't) happen. It LOOKS like an attempt to mislead prospective customers. If I bought an ALM based on these claims and found that the traces were obtained this way, I would claim fraud.
You can see the slope of the LC-1 signal is much steeper (faster) than the ALM. And, more closely matches the NB signal. It is just delayed several ms because of the sensor placement, further down the exhaust stream. Reverse the positions of the LC-1 and ALM sensors and you will get a very different result.
The variability in the delay that happens "sometimes" is based on the exhaust gas velocity at different engine speeds. No mystery here.
As for the LM-2, I don't remember if it has a full-speed signal output.
All wide-bands that use the Bosch CJ125 ( or CJ110,CJ120, or CJ135 ) have about the same SLOW performance. Which is quoted by Bosch ( t63 number ). If I remember right, the t63 is about 50ms. that is... it get 63% of the way to the right value within 50ms. That's the slow slope you see on the ALM trace. While the LC-1 gets 100% of the way to the correct value in 5ms or less.
To make my point. I have PERSONALLY used an LC-1 to tune individual cylinder carburettors on 12-cylinder ( 12 barrels of Weber ) engines. I can resolve individual cylinder AFR values at up to about 1500-2000rpm, using a scope. Try THAT with any CJ1xx based unit

BTW.... A LOT of times, that "noise" on an LC-1 at low rpm is variations in AFR between individual cylinders. Not something you want to "filter out".