Looking for these lifecycle dates for Entity Framework 4.0. End of Life Date End of Support Date End of Extended Support Date
Checked Microsoft page for Proucts lifecycle, however, EF 4.0 isn't listed there - https://support.microsoft.com/en-us/lifecycle/search
EF 4.0 is part of the .NET Framework version 4.X, which is still a current shipping product. It ships as part of Windows and follows the Windows support lifecycle.
See Lifecycle FAQ—.NET Framework
So, so long as you keep Windows updated and supported, your .NET 4 applications (including EF 4.0) will remain in support.
After EF 4.0, later versions were delivered as separate packages that relied on less and less of the .NET Framework components, so ironically EF 4.0 has a longer support lifecycle than any later version. So if you need any of the features that came in 4.1 (DbContext and Code First) and later, you must go all the way to EF 6.2 and keep current to retain support.
