A quick look at the source (HTTP/Request/Common.pm) reveals that if you pass a pre-formatted query string like this:

#!/usr/bin/perl

use LWP::UserAgent;

my $ua = LWP::UserAgent->new();
my $response = $ua->post("http://www.example.com",
    Content => 'var1=foo&var2=bar&var3[id]=foobar'
);
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it will not be touched any further by LWP. In other words, the square brackets will be sent literally in this case.

(Tested)