How planner decides left-anchored LIKE can use index

Exactly when does the planner decide that a left-anchored like can use the
index?

I have replaced a WHEN lower(last_name) = 'smith'
with WHEN lower(last_name) like 'smith%'

There is an index on lower(last_name). I have seen the planner convert the
LIKE to lower(last_name) >= 'smith' and lower(last_name) < 'smiti' on 8.2.4
systems, but a slow sequence scan and filter on 8.1.9 - is this related to
the version difference (8.1.9 vs 8.2.4) or is this related to something like
operators/classes that have been installed?

Carlo