Afternoon, I was asked to see why Excel 2013 would crash when attempting to sort/vlookup a large amount of data. Would updating the user to Excel 365 help to eliminate the crashed?
Microsoft made major improvements to the speed of lookup functions (including VLOOKUP) in the subscription version .... if you are doing many thousands of lookups on a million rows of data, the improvement can be a thousand-fold or more. Improvements were also made to make Excel more resistant to freezes, crashes and hangs.
I definitely recommend upgrading to Excel 2016 on an Office 365 subscription, especially given the reported problem. Excel 2019 (perpetual license version) will also have these improvements, but won't be getting any subsequent feature updates.