Lenovo won't sell you a new battery for it.

The T420 battery is literally just a bunch of off-the-shelf hobby cells run in serial. There's no reason to sell replacements, unless the little plastic enclosure holding it all together breaks.

That's not really what you would call supporting the device though is it.

Plenty of other ones will gladly sell compatible ones.

Buying 3rd party batteries is a nightmare, you never know what you are going to get.

Get it from known shops, and it is better than nothing at all.