1993lexusLS400

I spoke with a local mechanic and he thinks changing the fuel filter will help, although he can't guarantee that it will fix the problem. I do have a bit of trouble accelerating, so I think that is part of the issue (needing a new fuel filter). Thank you all so much for your help!

I'll start by saying my dash board is broken, so I can't see my speedometer, or anything else, and my gas gauge is broken. I am very good about keeping track of my miles and making sure I don't run out of gas. Well, I didn't get very good gas mileage last week because it ran out of gas on the freeway. To make a long story short, after filling my car back up with gas, it was running fine. So I drove it to work (40 miles) in the morning, everything was fine. On my way home, however, I was in terrible traffic (I live in Southern California so traffic is a daily nightmare) and when I came to a stop on the freeway, I turned my A/C off and my car turned off! The motor just shut down on it's own! So I put it in park, turned the key to off, then turned it back on and I was able to make it home safely by staying in the slow lane and driving incredibly slow. I want to take it into the shop today, but I'm hoping someone could give me an insight as to what I can do to fix it. I'm a 24 year old young lady, my grandma gave me this 1993 Lexus LS400 with only 100,00 miles on it, and I've only put 18,000 miles on it in the last 2-3 years. The car does perform differently with the air conditioner on, but it has never done this before! I just had the alternator replaced about 7 months ago, I'm not sure if that's important? I know this car is a gem and will last me at least another 100,000 miles, so I would like to learn as much as I can about this car and would like to fix it on my own! Please, if anyone can help me, I would greatly appreciate it!