Can BIG-IP LTM run on MS Server 2008 R2 with the Hyper-V 'role'?

yep. These deployment requirements should help you out.

Thank you for your quick response. Do these procedures also apply to version 11.5.0 ?

yes, there wouldn't be a procedural difference on hyper-v with regard to the TMOS version.

Thank you again Jason. I appreciate your quick response once again. Warm regards,Carol

Hi Jason, one more question. Where do I get an evaluation license for this? I downloaded it, created a VM and configured it>> Image fileset for Microsoft Hyper-V 2008/2008R2/2012/2012R2 - LTM-only on single installation slot BIGIP-11.5.0.0.0.221.LTM_1SLOT.vhd.zip