If you know your Roku password you can still log into your Roku account with your old email address -- it's just being used as a login name at that point so it doesn't matter if it's an active address.
The lost password reset function, though, will only send to the email address on record.
If you manage to log in, you can change your email address in the Account information section. This will update both your account login name and the account name shown via Settings > System > About.
Edited to add: I just changed my email address myself. It didn't 'take' the first time and I had to log in again and try a second time to get it to 'take'.
Roku Streaming Stick +, 3810X, Ser YH0059427035, wifi - Samsung UN55ES6100
Roku Streaming Stick, 3600X, Ser 5S56D8240827, wifi - JVC EM37T