How important is heat tolerance to you - do you prefer it cool or can you handle 30+ degrees?
Late September in Lisbon is still very warm, yeah, but for a lot of people it's just right. Temperatures usually hover between 25 and 28 degrees during the day, though it can hit 30 - nothing like July/August. The water's still nice because the beaches have been warming up all season. Your girlfriend's right that it's less relaxing compared to October and there are more tourists, but I wouldn't call it "too hot." It's way more pleasant than peak summer.
Prices really are better than July/August, and by late September you'll notice it's getting less crowded. Hotels and restaurants aren't as packed as before. The light is still fantastic, the days are still long enough. If you're not the type who breaks a sweat at 25 degrees, I'd say: go for it. You save money and still get decent weather for the beach and exploring the city.