Is it possible to use Lync on a private computer and connect with corporate accounts ?

Yes. If you have an account in that corporate work place, and have a lync client on your private computer then you will be able to access lync externally and interact with your colleagues.

It is important to note though that your lync environment will need to be configured for external access through the use of edge and reverse proxy servers etc.

If you are referring to corporate accounts of people outside your organisation, then the same answer applies, but you would need to be federated with said organisation.

The question leaves a lot of room for interpretation hence my assumptions. If you provide more particular details I can be more specific.

Regards
Ben