Floor it, and nothing...

[2001LC]

Turning at time of issue may have nothing to do with this. If transmission or ABS RPM should go up. If gas starved I'd expect some missing or sputtering.

I didn't think common after 99, but sounding more like limp mode.
I'm leaning towards TPS, AAPS or IAC along these lines now.

 

[ponytl]

You have a "throttle cable" on your 2000 BUT it's not what operates your throttle body, you are still throttle by wire... I think after 2001-2002 they did away with the cable completely... I would first check the wires/connection to your TPS usually you can stop and restart the engine and the issues will go away until it completely dies

 

[Julian Stead]

Have you read the ecus for fault codes, I would start with this. How long does the vehicle coast for, is it just a few seconds or do you need to come to a stop to reset it.