Yes, you create a Session object for the .NET Cil. For example, in VB.NET, use:
Dim m_session As Cisco.CtiOs.Cil.CtiOsSession
There is, however, no conversion function between Cisco.CTIOSCLIENTLib.Arguments and Cisco.CtiOs.Cil.Arguments as Cisco.CTIOSCLIENTLib is for the COM Cil and Cisco.CtiOs.Cil is for the .NET Cil.
As this is a programming development question, you may wish to join and utilize the Cisco Developer Network at developer.cisco.com
There is a technology center for CTIOS development at http://developer.cisco.com/web/ctios Once you join CDN (it is a requirement in order to obtain support for ICM environments where a custom CTI application is deployed) you will be able to post questions in the CTIOS Technical forum there.