Did your friend talk about what he likes about his A8 because there are notable differences to the S3?
If the Lexus and Audi are pretty even in your mind, then that's an opportunity to focus your decision on other considerations. Like the deal you can get between the two. Or maybe you do need to prioritize reliability, but rather than making it about potential costs, from the standpoint of whether you would prefer something you're less likely to have to worry about, if that better fits your lifestyle/personality/whatever. If you plan to keep this car as long as the Acura, there's a case to make for the Lexus.
Not sure I have great advice for the shopping part. I tend to make these kinds of decisions based on what I think results in the best blend of convenience and value that I can live with. I'm not somebody who is going hundreds of miles away to get the better deal. Mostly I get an understanding of the current market for exactly what I'm shopping for and try and come up with reasonable expectations about getting a deal done. There is plenty of info online that can help you determine what you should expect to pay for make/model in your location. If you're willing to be patient and it's not something that would feel like a hassle, you could track listings for local dealerships to get an idea about inventory volume and how quickly the models you're interested in seem to be selling, which can help calibrate your expectations about your cost, getting a car to your preferred specifications, etc. Since the S3 is an upmarket variant of the A3, there might be inventory limitations compared to the Lexus, but that's purely a guess. I just mentioned negotiating on warranties (likely there will be options for extended powertrain coverage, another for tires and rims, another for windshield, etc) because that's something I learned doing some research on a car purchase years ago that, admittedly, I wouldn't have thought of myself. There are also third party warranty options, though I don't have experience or recommendations there. I did once use a USAA extended coverage option to get a dealer to match the warranty cost which ended up being considerably cheaper. (FWIW, I don't think USAA offers extended warranties anymore.)