I'm by no means an expert, but I'll give you the little bit of knowledge that I have.
With regards to your last question: No, you don't need to connect Lync to a PBX/external phone system to make use of it. You can have Lync exist as an isolated communication system, and be able to have users send each other instant messages, audio calls, video calls, and multi-person conferences. However, in this scenario, only people using Lync clients will be able to communicate with each other with Lync. i.e. a person's desk phone won't answer when someone tries to call them with Lync.
As for the first part of your question, yes, you use some connecting mechanism to have Lync talk to your PBX/external lines. I'm not really a networking or phone guy, but the basic premise is that you would use a PSTN-to-IP PBX gateway to bring Lync into your infrastructure, and then configure Lync to point it to the gateway for external calls.