Looking at code from HOP::Lexer I found some interesting things. First an example (most of the code is the same from original post, I only change the data and lexer rules):

use strict;
my $sql = <<'--SQL--';
aaaa a baaaab a
--SQL--

use HOP::Lexer 'make_lexer';
my @sql   = $sql;
my $lexer = make_lexer(
    sub { shift @sql },  # iterator
    [ A      => qr/a+/i         ],
    [ BAB    => qr/ba+b/i       ],
    [ SPACE  => qr/\s+/, sub {} ],
);
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This gives us:

['A','aaaa'], ['A','a'], 'b', ['A','aaaa'], 'b', ['A','a']
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which seems wrong but: note that the rule A matches everytime the rule B matches (not exactly the same match but both match something) and, here's the surprise, HOP::Lexer uses split instead of matching the start of the string. This makes sense because you can have garbage or non-matched data at the start of the buffer, e.g. in original post example there's = which isn't matched by any rule.

Now it's easy to see why the rules work like that, for example with:

[ WORD      => qr/\w+/i        ],
[ DQWORD    => qr/"\w+"/       ],
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So, considering that split is used and WORD has precedence, always will happen that " will be considered what I called garbage. And that's why giving higher priority to DQWORD works (as I replied in the thread), because otherwise WORD would match the \w+ inside of the double quoted one.

As a rule of thumb: if a rule has other rule inside it, give it higher priority.