Are there any highly deadly spiders in Sri Lankan forests?

No, there are no highly deadly spiders in Sri Lanka that truly pose a lethal threat to humans. There are venomous types, such as the ornamental tarantula, but their bites are not fatal to people.

A bite from a large Sri Lankan tarantula or centipede may lead to localised pain, swelling, and muscle cramps. Still, it does not require anti-venom, and it will not kill you. In general, spiders on the island are naturally shy, mostly active at night, and they tend to avoid where people live, which means that bites are incredibly rare for tourists who stay in usual lodging.