Using one BIG-IP LTM chassis on two separated security network layers

You can do this with one Chassis. To separate the traffic, use Route Domains. You can define a Default Route per Route Domain, so traffic will separate the security zones.

To separate security zones adminsitrativly, you can use a Partition per Zone.

Route Domain Concept: https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/tmos-routing-administration-11-6-0/8.htmlconceptid