I just stumbled upon the fact that the font lmtt (latin modern typewriter) seems to exist in
- italic
- slanted
- bold
- bold slanted
but not
- bold italic
At least the file t1lmtt.fd contains the lines
\DeclareFontShape{T1}{lmtt}{m}{it}
{<-> ec-lmtti10}{}
\DeclareFontShape{T1}{lmtt}{m}{sl}
{<-> ec-lmtto10}{}
\DeclareFontShape{T1}{lmtt}{b}{sl}
{<-> ec-lmtko10}{}
\DeclareFontShape{T1}{lmtt}{b}{it}
{<->sub*lmtt/b/sl}{}
which, upon naïve use, leads to the rather unpleasant result

At the moment, my clumsy fix for this is
\input{t1lmtt.fd}
\DeclareFontShape{T1}{lmtt}{m}{it}
{<-> sub*lmtt/m/sl}{}
which means I get slanted typewriter (instead of italic) everywhere.
What would be a better alternative?
Mind you, I'm not complaining the bold italic font seems to be missing.
AFAICS the family cmtt doesn't really have any bold fonts anyway, so another obvious alternative would be to map bold italic to medium italic also for lmtt.