I'm using iTerm2 3.4.6 and vim-colors-solarized. For me,

echo `tput sitm`italics`tput ritm`

output italics without me having to update TERMINFO.

However, in order to get italics to work in vim, I still had to make two changes.

1. Edit .vim/colors/solarized.vim as recommended in Solarized #120 to replace lines 137-157 with the following:

    if has("gui_running") || ( has("unix") && system("tput sitm") == "\033[3m" )
        let s:terminal_italic=1
    else
        let s:terminal_italic=0
    endif
   

2. Edit .vimrc to add the following lines using <Ctrl-v><Esc> to enter the ^[ characters.

    " Enable italics
    set t_ZH=^[[3m
    set t_ZR=^[[23m
   

In addition to updating my TERMINFO, I had to make two other changes.

1. Edit .vim/colors/solarized.vim as recommended in Solarized #120 to replace lines 137-157 with the following:

    if has("gui_running") || ( has("unix") && system("tput sitm") == "\033[3m" )
        let s:terminal_italic=1
    else
        let s:terminal_italic=0
    endif
   

2. Edit .vimrc to add the following lines using <Ctrl-v><Esc> to enter the ^[ characters.

    " Enable italics
    set t_ZH=^[[3m
    set t_ZR=^[[23m