Lollipop has some serious changes in its SSL stack, and it can't connect to some servers (mail, web, etc) that previous Android versions could connect to.
This is a system level issue, not app level.
For the record, in my Dovecot config (Dovecot 1:2.1.7-7+deb7u1) I have:
# SSL protocols to use
ssl_protocols = !SSLv2 !SSLv3
But trying to tweak the ciphers causes SSL failures, so I ended up commenting it out:
#ssl_cipher_list = ALL:!LOW:!SSLv2:!SSLv3:!EXP:!aNULL