E2 means the Haier washer-dryer cannot confirm the door lock in the reference table consulted. Err2 refers to drainage: the two should not be confused.
The Haier Appliances documentation separates the two messages. The table mentions a 20-second locking attempt on those washer-dryers; do not use that timing to diagnose a different Haier model without its manual.
Closed door and locked door are different states
If the door can be opened and the drum is still, check for laundry caught across the gasket, too much pressure from the load, and visible latch damage. Close it without slamming. If the control panel still does not confirm the lock, do not keep pressing on the door to try to allow the cycle to start.
If there is water or heat inside, respect the latch hold and do not pull the handle. Unlocking is not necessarily achieved by cutting power.
When the outside is clear and E2 returns, request a check of the locking system. The display does not let you decide which component to replace or authorize bypassing the safety lock.
Indicate whether E2 appears before filling or after an interruption; service can then pinpoint the lock check.