Customer is agree to pay windows license in azure. if we do the lift and shift then what type of license he need in azure SQL server 2016.
In Azure if you build VM from azure marketplace which has image of Windows VM and SQL Server 2016 coupled together your Azure charges will include SQL Server charges and you do not need to pay for any license in Azure. you also have option to take SQL Server license in Azure.
EDIT
Quoting from the MS article azure-sql-iaas-vs-paas-what-is-overview
With SQL on Azure VMs, you can use any of the platform-provided SQL Server images (which includes a license) or bring your SQL Server license. All the supported SQL Server versions (2008R2, 2012, 2014, 2016, 2017, 2019) and editions (Developer, Express, Web, Standard, Enterprise) are available**. In addition, Bring-Your-Own-License versions (BYOL) of the images are available.** When using the Azure provided images, the operational cost depends on the VM size and the edition of SQL Server you choose. Regardless of VM size or SQL Server edition, you pay per-minute licensing cost of SQL Server and the Windows or Linux Server, along with the Azure Storage cost for the VM disks. The per-minute billing option allows you to use SQL Server for as long as you need without buying addition SQL Server licenses. If you bring your own SQL Server license to Azure, you are charged for server and storage costs only. For more information on bring-your-own licensing,
You can go to Azure market place and search for Image BYOL and then sql server version and OS version. You would get lot of supported images, use that image.