Commit is VERY slow in my NHibernate / SQLite project

Your transaction should be around the whole operation, not each save.

You would also then benefit from enabling ado.net batching: 1000

I think using session.evict() only covers the symptom. You haven't posted the GetSession()-Method but the comment above and the remark that session.clear() breaks your lazy loading makes me guess you are using one session for the whole application.
This is extremely inefficient and will slow down your app the longer it runs. Creating a new session on the other hand is really cheap and will provide you with a clean and fast session only handling the objects you want to.
IMO you should think about declarative transaction management. Personally i prefer Springs-TX-Management but there are also other clever solutions that aren't that method-based like for example castle's ActiveRecord.

You say that you have a List of measurement objects, but you are saving them 1 at a time. This would be fine, if all of the saves were in 1 transaction, but you have each save wrapped in a transaction. This will hurt your performance no matter how large the DB is.