What would you say CAPE has to be at for thunder? Around 250-300 and higher I think seems right, would you concur with that?
Yes Aaron, so long as the convective parcel can lift to atleast 7000m level before it strikes the tropopause or some other very stable layer. And it helps if most of the CAPE is in the lower part of the atmosphere, so the rising convective parcel gets some good acceleration on it before it hits less buoyant air. If the low CAPE is evenly spread through the depth of the atmosphere, as it is here in Auckland today, the convective parcel never gets into an evironment where it can really accelerate and turn conditions thundery.
The higher the CAPE, the better, for thundery weather.
CAPE is increased in 3 ways, often a combination of,
Rising surface temperatures,
Rising surface humidity (dewpoint),
Cooling upper air (trough, cold pool, divergence....)