So, when some who has been a paid members does not renew, send them a message 6 months after they lapsed.

You should be able to do this by having a mailer that is relative to the expiration date and configured to check 6 months after. Example as follows.

Automatically send message at following date: 6 months after
Relative to this date of the plans below: Subscription's Expiry Date
To which plans this date condition applies: SELECT_PAID_PLANS_HERE
Must be in state: Expired
But do not send message if it's later than: 7 months after

This has a 1 month window to avoid it sending to users that may have been expired for 3 years for example. Adjust as needed.

Joined at free level and never upgraded, email after 3 months

Is your free level a subscription? If so you can do a 3 month condition on the subscription date for the free plan. Example as follows.

Automatically send message at following date: 3 months after
Relative to this date of the plans below: Subscription's subscription Date
To which plans this date condition applies: SELECT_FREE_PLAN_HERE
Must be in state: Active
But do not send message if it's later than: 4 months after