This works. It actually works better without curry because then you don't need $object to be defined yet at compile-time.

use 5.018;
use strict;
use warnings;

BEGIN {
    package Foo;
    use Moo;
    sub meth {
        die unless ref shift;
        join "|", @_;
    }
    sub othermeth {
        die unless ref shift;
        join ":", @_;
    }
    $INC{'Foo.pm'} = __FILE__;
};

BEGIN {
    package curry::lexical;
    use Exporter::Lexical ();
    use Exporter::Tiny ();
    sub import {
        my $me      = shift;
        my $objref  = shift;
        my $optlist = Exporter::Tiny::mkopt(\@_);
        for my $method (@$optlist) {
            my ($name, $currystuff) = @$method;
            my ($originalname, @args) = ref($currystuff) ? @$currystuf
+f : $name;
            my $coderef = sub { $$objref->$originalname(@args, @_) };
            Exporter::Lexical::lexical_import($name, $coderef);
        }
    }
    $INC{'curry/lexical.pm'} = __FILE__;
};

use Test::More;

sub meth { "FUNCTION" }

is meth("foo"), "FUNCTION";

{
    my $obj = Foo->new;
    use curry::lexical \$obj, "meth", "meth2" => ["meth", "prefix"], "
+othermeth";
    
    is meth("foo"), "FUNCTION", "non-lexical sub wins";
    is meth2("foo"), "prefix|foo";
    is othermeth("foo", "bar"), "foo:bar";
}

is meth("foo"), "FUNCTION";

done_testing;
[download]

So with your example, you could do something like:

my $app = MyApp->new;

{
  use curry::lexical \$app, qw(log foo bar), critical_log => [log => "
+CRITICAL"];
 
  log("Hi");         # $app->log("Hi");
  foo();             # $app->foo();
  bar(123);          # $app->bar(123);
  critical_log();    # $app->log("CRITICAL");
}
[download]

The functions imported via curry::lexical cannot overwrite "normal" functions, as shown in the second test of the test script.