Well, now that is interesting. Let's assume that there isn't a change in engines or oil filters between your 350 and my '05 330. My car takes a standard steel screw-on cartridge. If that is the case, I would return this paper filter and then run away from that parts store. If they have changed filter designs then you might want to call Lexus service and ask them.
Frankly, I am guessing that your car takes a standard cartridge.
My biggest hassle in my first oil change was finding the &%3$ oil filter. Turns out that the Toyota/Lexus engineers hid it under the front exhaust pipe or the collector. I couldn't find it to save my life and I am an accomplished DIY kind of guy. I finally found it with help from this group. I now put the filter removal tool on by blind feel.
Let us know what happens.