Why is lemon mixed with water considered alkalizing water?
The claim that lemon water is alkaline is simply wrong.  However, that hasn't stopped people from claiming that it's true:


  Lemons are an incredibly alkaline food, believe it or not. Yes, they are acidic on their own, but inside our bodies they're alkaline (the citric acid does not create acidity in the body once metabolized). As you wellness warriors know, an alkaline body is really the key to good health.


Every sentence above is wrong.  Lemons do not turn alkaline inside the body.  They are not an alkaline food.  Citric acid creates neither alkalinity nor acidity in the body when it is metabolized.  An alkaline body is not the key to good health.  In fact, if your body were more alkaline by only 0.5 pH units from its usual state, you would probably die from it.


  I wanted to know the specific reactions that occur when mixing water and fresh lemon slices [...]


There aren't really many reactions that occur.  Lemon juice is mostly water.  Mixing the lemon juice present in lemon slices with more water just dilutes it.  Lemon juice is acidic, due to the presence of citric acid and other acids.  Diluting will very slightly lower the acidity.  None of that has any relevance to the pH inside a mammalian body, which is exquisitely regulated by other mechanisms.

I don't know why people make up weird claims that lemons are an "alkaline" food, but those claims, sadly, are out there everywhere.