The Church’s tech web site has a great article about the history of MLS:
In 1999, the Member and Statistical Records Department (MSR) began considering a rewrite of the local unit Member Information System (MIS) and Financial Information System (FIS). Since 1986 priesthood leaders had been using separate applications to manage local Church unit membership (MIS) and finances (FIS). MIS and FIS were available only to Church units in the U.S. and Canada and a limited number of English-speaking units outside the U.S. and Canada. In 1998, a separate tool, Convert Data Entry (CDE), was introduced for use by missions to submit convert information needed to create membership records. MIS, FIS, and CDE were developed in a text-based DOS environment. In April 2000, AP Software was contracted to help the Church in this rewrite.
There are a few screenshots of older versions, as well as some dates marking different milestones. Interesting stuff!