are lifters covered under the engine or drivetrain warranty

Since they are internal engine parts they should be covered. Extended warranty companies could exclude parts which are not covered but they has to clearly state this fact in their policy. Manufacturers generally cover the lifters under the drivetrain warranty, but you have to show them proof for all the manufacturer's suggested maintenance. If you missed services they can legally decline any warranty repair. Zee

Forget it, unless you have all the maintenance on record (repair invoices) nobody will help you. That meaning your oil changes documented every 3,000 miles.