So far I have never heard of a sebae anemone reproducing by lateral fission, at least not in our home aquariums. Unfortunately there is little specific information on all of the hosting type anemones with regards to reproduction. We do know of course that the bubble tip can be a prolific splitter (lateral fission), mine sure are.
Reproduction:
Spans the entire gamut, sexual and asexual. New individuals may form from a piece torn off during locomotion or trauma, by longitudinal or transverse fission.
Sea anemones may be separate sexes or hermaphroditic. If same ---, generally eggs and sperm tend to be produced at different times. Fertilization and some development may occur within the body cavity or not. Typically, anemone larvae have a planktonic developmental phase before settling.
So far the ones that I do know for sure split off the top of my head are, the BTA, Condylactis, and even the H. Magnifica can.
Thomas