I was in Argentina last February and discussed with a few people who had climbed Lanin right before (we were thinking about ascending it, but didn't in the end) and they didn't mention any specific regulations (but maybe there are).
One important thing is that even though it looks like an easy ascent, the weather can change very fast there and the way is full of crevasses. You can also get lost if it turns bad.
In fact strong winds come from the Andes, and bad weather from the Pacific ocean. Climbers have to be cautious there.
Try to get in touch with local guides for more acurate information, that's the best bet.
I climbed Lanin 4 years ago. There was a number of regulations, and be sure to investigate it, before leaving for the mountain. You have to bring ice axe and crampons, warm sleepingbag, down jacket, warm socks, warm gloves/mittens, warm hat, fleece, warm boots, head lamp - and a radio or sat. phone. It is possible to rent a radio at the station.
The climb was pretty straight forward, but the wind was hillarious. People disappear on the mountain every year due to the ever changing weather. We stayed the night in a hut on the way up.
John Biggar's book on climbing in the Andes says that if you're climbing from the Argentine side of the mountain then it is possible at the customs post @ Guarderia Tromen, "park wardens may ask to check your equipment and get you to complete some paperwork". He mentions nothing from the Chilean side.