LI's only nominally measure the temp difference between rising parcels of air and the environmental air at a single fixed height (typically 500hpa), whereas CAPE uses the height range of the vertical profile of the atmosphere over a given point where rising air parcels are warmer than the surrounding air.
So for example, if a rising parcel of air stays warmer than the surrounding air from when it condenses into cloud at say the 850hpa height right up to 300hpa, there's positive CAPE all the way from 850hpa up to 300hpa, and the amount of CAPE will depend on how much warmer that parcel will be than the surrounding air through that height range i.e. it's an integral.