I've noticed that monospaced fonts have uppercase Greek letters but no lowercase Greek letters. Is there a mathematical format to resolve this issue with monospaced fonts?
\documentclass{article}
\begin{document}
$\mathtt{\Gamma \Delta \Theta \Lambda \Xi \alpha \beta \gamma \delta}$
\end{document}
You don't get bold Greek lowercase letters with \mathbf{\alpha} either.
I can propose a \mathgreektt command, but you can't mix it with \mathtt.
\documentclass{article}
\DeclareFontFamily{U}{greektt}{}
\DeclareFontShape{U}{greektt}{m}{n}{
<-6> gttn0500
<6-7> gttn0600
<7-8> gttn0700
<8-9> gttn0800
<9-10> gttn0900
<10-12> gttn1000
<12-17> gttn1200
<17-> gttn1728
}{}
\DeclareMathAlphabet{\greektt}{U}{greektt}{m}{n}
\NewDocumentCommand{\mathgreektt}{m}{\greektt{\changecodes#1}}
\ExplSyntaxOn
\NewDocumentCommand{\changecodes}{}
{
\tl_map_function:nN
{
{{\Alpha}{A}}{{\Beta}{B}}{{\Gamma}{G}}{{\Delta}{D}}{{\Epsilon}{E}}
{{\Zeta}{Z}}{{\Eta}{H}}{{\Theta}{J}}{{\Iota}{I}}{{\Kappa}{K}}
{{\Lambda}{L}}{{\Mu}{M}}{{\Nu}{N}}{{\Xi}{X}}{{\Omicron}{O}}
{{\Pi}{P}}{{\Rho}{R}}{{\Sigma}{S}}{{\Tau}{T}}{{\Upsilon}{U}}
{{\Phi}{F}}{{\Chi}{Q}}{{\Psi}{Y}}{{\Omega}{W}}
{{\alpha}{a}}{{\beta}{b}}{{\gamma}{g}}{{\delta}{d}}{{\epsilon}{e}}
{{\zeta}{z}}{{\eta}{h}}{{\theta}{j}}{{\iota}{i}}{{\kappa}{k}}
{{\lambda}{l}}{{\mu}{m}}{{\nu}{n}}{{\xi}{x}}{{\omicron}{o}}
{{\pi}{p}}{{\rho}{r}}{{\sigma}{s}}{{\tau}{t}}{{\upsilon}{u}}
{{\phi}{f}}{{\chi}{q}}{{\psi}{y}}{{\omega}{w}}{{\varsigma}{c}}
}
\__siri_change:n
}
\cs_new_protected:Nn \__siri_change:n { \__siri_change:nn #1 }
\cs_new_protected:Nn \__siri_change:nn { \cs_set:Npn #1 {#2} }
\ExplSyntaxOff
\begin{document}
$\mathgreektt{\Alpha\Gamma\Delta\alpha\beta\psi\omega\sigma\varsigma}$
\end{document}
fix-cm.sty and used gttn that's the monospaced font in CBGreek. Then applied the translitteration used with LGR encoded fonts.
\alphais set up as a symbol like+so would not change font under\mathtteven if the font had an alpha. But you have not shown what fonts you are using