Hi seoanalytics
Lexical semantics and synonyms are similar in that, whilst a synonym is one word which can be substituted for another - Bike / Bicycle - Lexical semantics deals with the meaning of the word or phrase.
A bike or a bicycle is a machine for conveying a person from one destination to another. The meaning of the word is that it is a self-propelled mode of transport. A synonym of a bike is simply 'a bicycle' - no need for any explanation.
LSI or latent semantic indexing is an old acronym that really shouldn't be used in relation to modern semantics. It was originally used in the 80's as a way of indexing complex information. A form of data retrieval - most high-level SEOs completely poo poo its use these days so it's best to ignore LSIs and focus on the concept of semantics in its true sense.
I think the danger here is that you risk getting bogged down in the subject and over optimising your page. The essence of great writing can be lost in a desire to fill the page with every conceivable permutation of synonym and lexically connected words and phrases. In doing so you risk either over stuffing or getting it wrong. Worse still, spending just too much damn time on it!
The topic is the place to start as that is the highest level. So the topic, for example, is Bike Tours In Piedmont.
Synonyms can simply include the words Bicycle as opposed to Bike and for example Routes and Trails.
Semantics are the wider meaning - so 'Biking through Italy'
In my reply on Dec 22 I said that you must focus on 'what people might type in' and what you are seeing in the Google suggestion tool and the related searches at the bottom are firstly the most common words and phrases typed in and secondly what Google believes are closely related searches.
Like I have said all along - don't get too bogged down in this - the knowledge you have learned here is likely to be 100 times better than any other site competing with you - trust me! No one I have ever helped has gone into this subject as deeply as you! So you will be miles ahead!
Related topics are separate pages - don't mix them up. It's very much in the writing of the sentences so when I use the word 'pepper' this means intertwining or 'sprinkling' it into your content.
Finally, if someone bangs on about LSIs then ignore them as they do not know what they are talking about. Too little knowledge is a dangerous thing.
Regards
Nigel