Lymington really is a great place to live. I grew up there and still live nearby.
I know a few people who have property on the high street and just off of it. Both have parking however there are a few long stay car parks around the high street which from memory allow you to park there for 20 hours - that might be a solution if the property you are looking at has no parking.
You can purchase long stay clocks which can be used across many of the NFDC car parks, I believe they are approximately £35 per quarter but money well spent! Within the last year or two they have changed the parking on the high street which now requires you to purchase a ticket up to a maximum of 2 hours I think. As a previous poster mention, no parking on a Saturday though and it can be a bit of a nightmare in the summer with many people walking on the road. Becomes very busy with tourists in the summer too.
As with any high street, there can be noise but I've never known it to be a problem in Lymington. It's a great location as lots of nice restaurants both on the high street and on the quay. There's a real mixture of shops too.
The high street is within easy walking distance to the train station which will take you straight to Brockenhurst which has some great restaurants. Bear in mind the trains do stop just after 10pm though.
There's plenty of places to walk & relax within the town including along the sea wall which will take you to Keyhaven but further a field you are spoilt for choice with beaches & the forest.
Overall, I can't really say anything bad about Lymington, it was a lovely place to grow up and I still visit family regularly who live there. Hopefully if you do buy there, you won't regret it!