my $str = $change_in_place && $default_argument ? $_ : $_[0];
$str =~ s/^($lchompstr)*//;
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I think this would (in the case $change_in_place && $default_argument) change only a copy of $_, not $_ itself. Maybe one could somehow use a foreach loop iterating over a one-element list, but I don't see how this would work in the general case.

I think that you could just take advantage of the fact that “ternary conditionals preserve lvalue-ness”, and write:

($change_in_place && $default_argument ? $_ : $_[0]) =~ s/^(?:$lchomps
+tr)*//;
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(I've taken the liberty of making your parentheses non-capturing. :-) ) I'm not sure why you end with the $_[0] statement, though—it seems that you're returning the first argument even if you ignored it (because of $change_in_place and $default_argument).