Southport will be the last line to get them, the roll out is expected to be.
Ormskirk
Wirral
Southport
The new trains have to be tested first after being delivered to Kirkdale TMD, they have to go through fault free testing before entering service [think it's 500 miles of fault free testing], when you think how many trains are being delivered, the network itself isn't that big, in terms of mileage, it is going to take time, so not sure how long the full roll out is going to take.
Kirkby is first line to have them, mostly as it's the shortest line & it's not far to Kirkdale TMD, if any faults develop in service.
Most faults can be found in testing, but others [like any issues with the doors] can only be found when in service.