So does VMnet4 have a gateway set? can your lamp server, see (ping) the gateway? can your big-ip, see (ping) the gateway?
From one thing, its been a couple of years since i used workstation, but not sure what "custom" does.
I would have said you wanted a Host-only network, or least test it with that first.
My first guess is that this is a workstation / network interface issue. So also check your mac addresses under Network > Interfaces and make sure they align to your workstation config of the interfaces you have assigned.