I compile my document with xelatex. I use Myriad pro
\setmainfont[Mapping=tex-text]{Myriad Pro}
My problem is that the "l'a" is looking OK but not the "l'i" the i touches the apostrophes. Can someone tell me how to fix this issue?

There is nothing wrong with the font, you can find this out by writing the same thing into another program. It is a issue with ICU engine with XeTeX.
One way to fix it is to issue a zero kern after the apostrophe:
l'\kern0pt inno

Another option would be to use \XeTeXinterchartoks to insert that kern automatically.
See this answer on how to do it.
Here's an example as requested:
\documentclass{article}
\usepackage{fontspec}
\setmainfont[Ligatures=TeX]{Myriad Pro}
\XeTeXinterchartokenstate=1
\newXeTeXintercharclass \aposclass
\XeTeXcharclass `' \aposclass
\XeTeXinterchartoks \aposclass 0 = {\kern0pt }
\begin{document}
L'arbre de l'inno
\end{document}
:(kerningfeature will be back inmicrotypefor Xe/LuaLaTeX someday.