Hi @gafhdrz,
Unfortunately the batteries for the two model ranges are not interchangeable between the models.
Here are images showing the Lenovo part numbers (FRU number) for the 11 batteries that are compatible with the Yoga x1 2nd Gen Type 20JD laptop and the 3 batteries that are compatible with the Yoga x1 3rd Gen type 20LD laptop. (FRU = Field Replaceable Unit)
Type 20JD
Type 20LD
(click on images)
To find a replacement battery for the 20JD laptop, search online using the part number only (any one of the 11) to get results for suppliers that suit you best.
If you have the Lenovo Vantage program installed in the laptop it will tell you information regarding the battery in the laptop e.g. what your battery percentage is at alongside it's charge capacity, model number (part number aka FRU number) and manufacture date. You can compare the FRU number with the list in the image above.
Here's the hardware maintenance manual for the Lenovo Yoga x1 2nd Gen 20JD laptop. Go to p.73 to view the procedure to remove the battery.