I have,
Now, I would like to create asp.net Core web app with dotnetcore 2.1
and want to reference the class library.
Do I need to,
Yes, you have to convert you libriary to .NET Standard in order to reference it from both Framework and .Net Core apps
You would need to use .NET Standard version 1.2 or lower in order to support .NET Framework 4.5.2
See the documentation for details: https://learn.microsoft.com/en-us/dotnet/standard/net-standard#net-implementation-support