How can I access a dynamic variable while a similarly named lexical is in scope?

You can do this via symbolic references, provided you haven't set use strict "refs". So instead of $var, use ${'var'}.

    local $var = "global";
    my    $var = "lexical";

    print "lexical is $var\n";

    no strict 'refs';
    print "global  is ${'var'}\n";

If you know your package, you can just mention it explictly, as in $Some_Pack::var. Note that the notation $::var is not the dynamic $var in the current package, but rather the one in the main package, as though you had written $main::var. Specifying the package directly makes you hard-code its name, but it executes faster and avoids running afoul of use strict "refs".