Batteries are only covered under warranty for one year and are not covered under the accidental damage protection.
The part needed has a description of internal,4c,35Wh,LiIon, SIM. The Lenovo part number is 45N1751 or 45N1749 or 01AV404.
Listed below are several purchasing options If you buy it, we will install it for you.
You may purchase one directly from Lenovo for $78.78. Go to https://support.lenovo.com/us/en/partslookup and change the dropdown menu to look up by Part Number. Enter 45N1751 in the look up field to locate.
Newegg has it for $51.39 - https://www.newegg.com/Product/Product.aspx?Item=9SIAAMU58U3621 and $49.89 https://www.newegg.com/p/16J-00F6-097G7
You may also locate one on eBay or Amazon by searching for it by part number.
Amazon has an off brand for $40.99. https://www.amazon.com/Binger-45N1748-Replacement-Battery-ThinkPad/dp/B06XJRQ3VR/ref=sr_1_1_sspa?ie=UTF8&qid=1543856336&sr=8-1-spons&keywords=45N1751&psc=1 or https://www.amazon.com/ZTHY-Compatible-Replacement-ThinkPad-45N1750/dp/B00XXO2V8O
Amazon has this off brand for $39.22 - https://www.amazon.com/ZTHY-Compatible-Replacement-ThinkPad-45N1750/dp/B00XXO2V8O/ref=sr_1_2?ie=UTF8&qid=1543856669&sr=8-2&keywords=45N1749
Bestbuy has this off brand for $39.99 - https://www.bestbuy.ca/en-ca/product/laptop-battery-for-lenovo-45n1750-2icp6-50-702-2icp6-50-70-2-45n1748-45n1749-45n1751/13048799.aspx