Some alternatives:

≥ 5.10

$lala =~ s/([a-z])\K\1//g;
[download]

See the perlre for 5.10 (or the one for 5.9.5).

< 5.10

use Regexp::Keep;
$lala =~ s/([a-z])\K\1//g;
[download]

See Regexp::Keep.

Update: Added links to documentation as privately requested.