The LAN_ENTERPRISE_SERVICES_PKG license has nothing to do with HSRP. LAN enterprise covers: OSPF, BGP, IS-IS, PIM, SSM, MSDP, Policy based routing, GRE tunneling, EIGRP, VRF route leaking, VXLAN and BGP eVPN.
HSRP requires no license. Any feature not included in a license package is bundled with the nx-os image and is provided at no extra charge. To activate HSRP simply use:
switch(config)# feature hsrp
Nexus 9000 series HSRP configuration guide:
As rnxrx has correctly mentioned in the comment, there's a difference between the Nexus switches and what basic features are supported. Therefore i've added the below license matrix for all Nexus switches and all licenses possible to add: