Hey there,
I wouldn't worry too much about the concept of LSI. Most of the people who know it well will tell you that it's a valid concept, but not used actively by Google (https://twitter.com/bill_slawski/status/963525512294379520).
LSI are synonyms of the keyword your target (the one in the H1 and title tag). For example my keyword would be "Tuscany bike tour" and my LSI would be "Tuscany cycling vacation", "bicycle tour in Tuscany" etc...
Then secondary related keyword are for me the other topics I need to cover in my content. In this case for example it would be "Florence", "Siena". But from what I understand a good writer wouldn't use "Siena" or "Florence" multiple times in it's content it would replace it by keywords that support them such as "the town of Florence", "the city of Siena"," the Palio of Siena" etc...Is my understanding correct ?
I disagree with that. While you don't want to use a term excessively in a piece of content - there's no problem with using it multiple times, and writers should use variations naturally. Also - you don't need to think of "town of Florence" and "Florence" as separate keywords. They're close enough to be interchangeable. Usually when SEOs talk about related terms, they're talking about "world war II" and "germany", or "trees" and "leaves".
If so what is the use of using those secondary related keyword, is it to rank on other keywords such as Palio of siena tuscany bike tour ? or just not to repeat a secondary keyword too many times. If i write the Palio of Siena isn't it considered as another topic that the topic siena ?
An article about a bike tour in Siena should be a separate piece of content from an article about the town of Sienna. It appears that "palio of siena" is a horse race? In which case that would be two separate pages of content if you wanted to rank for both terms.
I recommend looking at some established and top-ranking websites in your niche and see what they're doing. That's often the best way to get a feel for what is working. If your niche isn't super competitive and you can't find examples you think are good, you can also look at more competitive topics in related industries - for example "kentucky derby"-related searches might be a good example in the US.