The records of the London Missionary Society are held at the library of the School of Oriental and African Studies in London.

Some of these documents have been copied on microfilm by the Pacific Manuscript Bureau in Canberra.
http://asiapacific.anu.edu.au/pambu/

If you search on "London Missionary Society" you will see what has been microfilmed. The only baptismal records seem to be for Niue. The other records are relating to the organization itself and the European missionaries.

These Pambu films are held in various large University Libraries around the Pacific region.

In 1844 the London Missionary Society established Malua Theological College at the village of Malua on Upolu to educate local men to become village clergy for the rapidly growing mission with over 250 villages and 25,000 membership.

Perhaps Malua College, which still exists, and has a good library, may know where Samoan baptisms are, if they still exist.
Christine