The first question would be which version of LTM are you trying to install? The network stacks/drivers have changed between versions.
There are a few different ways to do this, based on preference, but I'll tell you how I do it.
1. Your VM needs at least TWO network adapters. The first in the list will always be your management port. I like to create several adapters and set them as host-only, and then one other assigned to the NAT. Doing host-only allows you to isolate the networks in your lab. I may also choose to NOT "Connect a host virtual adapter to the network" for some networks, which would otherwise create an adapter on my local machine, so that I can only access those networks through the LTM (or other routing device). I'll use the NATted adapter as my route to the world through VMware's NATted interface to my host machine's Internet connection.
2. Install VMware via ISO or the VE .ova. The .ova will have most of the above already done for you and is infinitely easier to set up. You want to make sure that after the install the second and subsequent interfaces have assigned MAC addresses. If no MAC assigned, then nothing else matters. Again, the .ova will do most of this for you.
3. Once you have connectivity to the management GUI via the management network, and assigned MACs on the other interfaces, start setting up your VLANs and self-IPs. One oddity of Workstation that I've come across from time to time is that the interfaces aren't in any order. Generally you can look at the list of interfaces in the VM's config and go by that order, but sometimes not. The first one will always be the management port (or you wouldn't be able to get into the GUI), but the others could be in different orders. So what I do, if the specified order doesn't seem to be working, is to create my VLANs without any interfaces assigned, create the Self-IPs and attach to the VLANs, then start a ping from my local machine to the Self-IP as I add and remove interfaces from the VLANs (one at a time). Between tests you'll probably need to clear your local ARP cache (arp -d *). In the end you should be able to ping each of the Self-IPs.
4. As for the NATted interface, you'll want to give it a static Self-IP in the subnet that VMware Workstation uses for its NAT. In my lab that's 192.168.247.0/24. You can then create a route out to the world by building a default gateway (0.0.0.0/0) that points to the .1 IP (ex. 192.168.247.1) of the NATted subnet, and DNS is usually the .2 address. Test by issuing either an nslookup or curl statement from the command line to something on the Internet.
Give that a shot and let us know how it goes.