The LS has anti-dive front/anti-lift rear suspension geometries, so it doesn't have a great deal of nose dive on hard braking. It sounds like your brakes are engaging too far into the pedal's travel though.
It's entirely possible that you need new brake pads; the more worn the pads are, the lower the brake pedal will go before engaging. I doubt that the difference in travel will be particularly noticeable, though, so it may be that you need to bleed the brakes.
Switching to different brake pads (like Porterfield's R4-S) will also help.