If all you want to do is to extract data between each >lmo, you could do this instead:

local $/ = '>lmo';
while (<DATA>) {
    s/\n*?>lmo//;  # add s/\n//g; if you want to combine lines
    next if !$_;
    print "--- REGION ---\n", $_, "\n";
}

__DATA__
>lmo0024        16802072 upstream sequence, from -300 to +3, size 304
ctttcggacaaagcgtggttgattttattcttaacgaaattccagaatggctaatgggtg
caaaaatccagtagctgcaggagcaaatggtgcagcgctagttggggaggaga
atga
>lmo0025        16802073 upstream sequence, from -27 to +3, size 31
aatataaaaattggaggaatagacaaaatgg
[download]

And the output -

--- REGION ---
0024        16802072 upstream sequence, from -300 to +3, size 304
ctttcggacaaagcgtggttgattttattcttaacgaaattccagaatggctaatgggtg
caaaaatccagtagctgcaggagcaaatggtgcagcgctagttggggaggaga
atga
--- REGION ---
0025        16802073 upstream sequence, from -27 to +3, size 31
aatataaaaattggaggaatagacaaaatgg
[download]