I’d have to think of more examples to be sure, but I’m not certain you’re right.
The ‘s’ is a /z/ in both lasagne and caso – it’s the same sound in both words. What he (mistakenly) said was /t.ts/ – that’s the “pause” in the double-consonant “zz” in cazzo.*
In any case, the pronunciation of single and double consonants is a little tricky to master, as you say. Also the pronunciation of both ‘s’ and ‘z’ in the middle of words is heavily regionally influenced.
*Edit: Wikipedia tells me that this “pause” is called Germination
