How to cope with lab noise?
Is this situation actually normal?


Yup, pretty normal. It's what is called "office life".

I am almost tempted to vote to close this as a boat programming question, as it is really no different to any other "we-are-in-a-shared-office-but-my-office-mates-annoy-me" situation in any job. Anyway, I think this is common enough in academia that it may make sense to answer here.

Essentially, there are really only three ways to fix this:


Change the office layout. Either get smaller offices (very unlikely to be possible), or re-arrange the PhD student seating so that the quiet workers share offices as well as the enthusiastic discussers. Of course, if you have one big lab for all students, this solution is probably a no-starter (not common here in Europe, but I have learned that this is common in the US).
Home office. Probably the easiest, most immediate, and most common solution to the problem of the annoying other students is to spend more time working from home or another suitable location, especially if some high-concentration tasks are in the queue. Of course this requires a modicum of trust that PhD students that are not in the lab are actually still working, and not sleeping or using their XBox. Given your concern that you may appear as "not working enough" when you are not in the lab, this may indeed be a problem.
Noise cancellation. When we had this problem in our lab, the easiest fix was to buy a set of high-quality noise cancellation headphones from Bose. The ones we bought are massive enough that even just wearing them alone without any music already blocks out a lot of the regular room acoustics, and they are high-quality enough that you can wear them for hours without pain. Students that want to work now wear their noise cancellation gear, which incidentally also is a good "Do not disturb unless important" sign for other people that just want to chat.


I should mention that "talk to the other students and make them stop" isn't really a practical and permanent solution. There are just too many people with too many differing characters for too many hours a day in a typical PhD student office - if somebody is the chatty type, she or he will chat.

Btw., I feel for you. My productivity when I am alone in my office is twice of what it is when we are two persons, which is again twice of what it is when we are three. I was never in an office with more than three persons, but I presume I wouldn't even need to bother coming in. This Dilbert comic strip is representing my feelings regarding the current trend of "open floor plan offices" pretty well.