Do I need a sub?

Short answer. Any system will benefit with use of sub(s). Biggest gains will come from using high pass filtering on main amp. Let sub amp do all the heavy lifting. This will benefit SQ all the way around, not just adding hertz on the bottom end.

Arc, Mr-m has it right. Every system benefits from subwoofers unless they are already built into the main speakers. Do not bother with a single small sub. You will not be happy. Two 6" drivers can go extremely loud if you remove 100 Hz down from them. You need at least two 12" or four 10" subs to get anywhere. Most subs now come with plate amps and cross overs in them. You absolutely need a crossover with a high pass filter for your main amp as you suggest. Unloading the main speakers is one of the major benefits of using a sub. You will clean up everything else those 6" drivers carry. For those of you who do not believe in Doppler distortion just have somebody drive by you at 30 mph leaning on the horn. The sound will go from a high pitch to a much lower pitch as the car passes you. Towards you and away from you just like a woofer pumping away changing every other note it carries. 
richtruss, the Lyngdorf is a crippled version of Radomir Bozevic's original design. The Trinnov is much better but still not up to Bozevic's design in some ways.

You need 4 subs minimum! 

Minimum.
Zardoz....Is your dog by any chance telepathic?

I suppose most A’gonner’s live in suburban houses where bothering neighbors isn’t as much an issue for city dwellers like me. You might however have to contend with bothering people in the house.

Bass is the hardest thing to contain as bass waves are close to 30 feet or longer.

So you might want to consider the ability to easily tailor how much bass any prospective sub is putting out. It really comes in handy, in that you can fill out a bass shy recording, or add a little bass if listening at low volumes, cut it down at night if there is the possibility of disturbing other people.

All the other posts here are great advice about getting the best bass, but I thought I’d point out something else to consider.