/\$\$/ {
    N;
    /\\begin\{align\}/ {
        s/\$\$//;
        p;
        d;
    }
    /\\newcommand/ {
        N;
        d;
    }
}

/\\end\{align\}/ {
    N;
    /\$\$/ {
        s/\$\$//;
        p;
        d;
    }
}
s/lightgreen/LightGreen/g;
s/:::/::: /g;