Try this. Find 1 or 2 comparable chain gyms around you (24hr fitness, golds gym) and 1 or 2 local gyms that have a few less amenities and cost a little less. Check them out and get their pricing. Then come in to LA Fitness and tell them that you have been looking around at other local gyms (tell them which ones) and tell them you are interested in checking out LA fitness.
When they take you on the tour and ask you what you are interested in, tell them you're only coming here to lift weights. The membership counselor will try and sell the extra pricing they want to charge you with amenities like the swimming pool, newly remodeled locker room, sauna, spa, basketball court, racquetball courts, cardio rooms, and various other things that those other local gyms might not have. If you only show interested in the weight room, they will realize they can't charge you top dollar, otherwise you will choose one of those smaller and cheaper local gyms that may not have all those amenities.
Once the tour is over, they will give you the prices (high initiation and low monthly fee, medium initiation and medium monthly fee, or no initiation and high monthly fee). Based on what you know about similar gyms in the area, come up with a low ball price (usually their lowest monthly fee and no initiation) and see if they will give it to you. Make sure you tell them that you are ready to sign up right now, this very second, if they agree to your price.
Membership counselors are paid on commission, and it's not necessarily proportional to the price you pay. In other words, they typically will get a similar commission whether they sell you a gym membership for $30/month or $40/month, but obviously they will get no commission if you choose another gym. So they are more motivated to sell you a membership, and not as motivated to sell you the most expensive membership.
If you haven't talked to the sales manager, you probably aren't getting the lowest price you can get. They will sometimes tell you that a certain price is the least their computer allows them to offer you, but there are always other rates. They might be able to give you a student rate. If you work for a corporation, they may be able to give you the corporate rate (even if your company is not on their list of employers who get a discount). I've even had a friend get the "current member who is about to cancel his membership unless we offer him this amazing deal" rate. Just keep asking and they can find something for you. Don't be afraid to negotiate. It's very normal at the gym for two people to pay 2 completely different prices for the same service. It's all about how you negotiate.