I often laminate brand new posters or ones I have had for a few years that I have decided to keep. However, paper posters that are 30 years old probably have degraded somewhat and lamination will not stop that process. In theory aper needs protected in an acid-free environment in terms of keeping things for historical purposes or to pass on to the next generation. For your own personal enjoyment, lamination should be fine and will provide protection.

You might talk to an archivist at a local museum and get advice or even a good copy shop might be able to advise. [or google it, lol]