Whether it's worth it to go through the trouble of getting "as built" permits for your LR depends on where you live, how well the addition was constructed (is it "to code?"), and whether having the extra square footage permitted will add value ($) to your property.
Even if you're not planning on selling the house for a few years, it wouldn't hurt to interview a few realtors and ask for their advice now. Just be up front with them when you contact them. You may also benefit from paying for an appraisal. An appraiser could tell you:
1) How much would the property be worth if you do nothing other than disclose to potential buyers that there is an unpermitted addition?
2) How much would the property be worth if you went to the trouble and expense of getting after the fact permits for the addition?
If the house would be worth about the same whether the LR is permitted or not, then there's no sense going to any trouble to get the permits. If the house would be worth considerably more if all the square footage were permitted, then it may be worth it to consult some general contractors to get their advice on how difficult it would be and how much they would charge you to get the place permitted. If the two numbers are close, probably it's not worth stirring up what could end up being a lot of trouble by alerting the bureaucrats to the fact that your home contains unpermitted additions.
My wife and I just sold a home that had ~700sqft of unpermitted additions. We thought about going through the process of getting after the fact permits for the additions, as they were all built to code or better, but it turned out that it probably wouldn't have been worth it in our case. Even without the permits our home sold for the same price as the last highest sale in our neighborhood in the previous 6 months.
If we had gotten the permits, our realtor said, we could probably have asked and maybe have gotten a little more money, but our place would have been harder to sell and it would probably have taken longer because we would have been asking buyers to pay more than any other property in our neighborhood had sold for in the recent past. Our realtor recommended we just fully disclose everything to potential buyers and not bother getting any permits, which in hindsight turned out to be good advice. The buyers loved our house and were fine with the fact that part of the house was unpermitted. They had an appraiser come in, and I'm sure he told them that every part of the house, permitted and unpermitted, was extremely well built, actually over built, and that it was worth the price we were asking. Our house was only on the market for about 3 weeks before we got an all cash offer that was within about 5% of our asking price.