Is it possible to connect to LYNC Server 2013 from outside without public certificate

Question

Hello to everybody
I have a rather simple question but i cannot find a definite answer
I have installed Lync server for purely testing purposes on my work lab
I have internal communication ...even web based but i don't know how to get external communication
I have a domain with FQDN : domain.abc.com    .... please
take note that the FQDN is 3 part...my computer are registered under computer.domain.abc.com.....and my domain is presented as
abc
My lync server is lsvr.domain.abc.com
We also have DNS records to external.abc.gr pointing to my static IP
Is it possible to create a self signed certificate that will enable us to perform external communications...especially with the Lync Web app or i should
definitely get a public certificate.
The whole issue is that we wish to make a presentation to the company's owner in order to get the approval to buy Lync and the required infrastructure or will use some other way of communication like Skype
It seems i cannot get a definite answers if i can do it without paying the money for the certificate or we should bite the bullet and pay the certificate

Answer 1

Well i had a mistake in network configuration but now i have different issue and i can't find how to begin with this
Let me take it from the beginning ...
I am user :Tsuser
I connect internally to my Lync Server :lsvr.domain.abc.com
with internal IP 192.168.1.200
I use
the meet url : https://meet.domain.abc.com/Tsuser/randomnumbersletters
I connect
ok
I change
the meet url to : https://Internal IP of lsvr(192.168.1.200)/Tsuser/randomnumbersletters
i get 404  File or directory not found.
I change
the meet url to : https://lsvr.domain.abc.com/Tsuser/randomnumbersletters
i get 404  File or directory not found.
I port forward my public ip to lsvr.domain.abc.com
port 4443 the same 404
Something is wrong here but i can't figure it out
Can anyone give me a helping hand...i think this is the main obstacle