To my knowledge, you will still need an annulment. If your ex was Baptist, his baptism (if he had one) may not be considered valid. It may just the short form. You might check with Jerry. He understands the ideosyncracies better than I do. At the very least, he explains them better!
Assuming Leslie was Catholic at the time of the second marriage (which I presume because she petitioned for an annulment for the first marriage) and if the second marriage was performed outside the Church without dispensation from the local ordinary (bishop or archbishop), then she should be able to use the "short form" process for lack of canonical form. This is a fairly quick process (6-8 weeks or less) that involves submitting some paperwork; there s no investigation beyond validating that the facts presented are accurate.
The requirement for canonical form applies to all marriages where at least one spouse is Catholic, regardless of the faith or baptismal status of the other party. The baptismal status of the spouses affects whether the marriage is sacramental, but not whether it is valid: even two non-baptised people can have a valid marriage and thus not able to receive a decree of nullity (aka annulment). There are some situations where a valid marriage between at least one spouse who was unbaptized may be dissolved under the Petrine or Pauline privileges. This is fairly rare because of the very limited circumstances under which these privileges apply and because the process is handled in Rome and can be very lengthy. For this reason, the marriage tribunals usually recommend going through the annulment process first.
Leslie, the first person to contact is your parish priest or the designated contact in your parish. But do be aware that, as someone else noted, many parish priests are not very familiar with the process and may give you an incorrect answer (in either direction). If you are told something different that what we've told you here, check directly with the marriage tribunal for your diocese, who are the authority on these matters. This is especially true if you are told you don't need an annulment because you were married outside the Church.