Low power + LS35a doesn't seem like a good match to me. The Tripath power ratings go down as impedance goes up, from memory you'll get maybe 4 wpc of clean power at 15 ohms. With the LS35a efficiency (again from memory) of around 85 dB/w/m, you'd be pushing to break 90 dB in room.... Your situation would be worse, I'd expect a case of audio constipation. I'd look for 100 wpc minimum to go with the LS35a's. I ran as similar combo 20 years ago with very good results.
My experience with LS3/5A's has been very different. I have found that LS3/5A's, despite their 82dB efficiency, are very easy to drive. I've owned a pair of 15-ohm Rogers for over 25 years and a pair of 11-ohm Spendors for over 10 years. I've run them with many different amps, mainly tubed, though recently with Tripath-based amps. They sound best with moderate-power tube amps such as the Dynaco Stereo 70, the Quicksilver Minis, the cj MV-50, and Musical Reference RM-10. Remember, LS3/5A's were not designed to handle lots of power. To my surprise, they also sound terrific with SET 300B amps of only 8 watts, such as the ASL AQ-1005DT. They can play so loud, in a large acoustical space that includes living room, dining room, and kitchen, that my condo neighbors ask me to turn them down. I have subsequently learned that in Asia many LS3/5A aficionados consider the pairing with a SET 300B amp a heavenly marriage.
In my 12x14' bedroom I have my Spendors driven by a Trends TA-10, a Tripath amp that is probably only 6 watts per channel. It is a wonderful combination also, although less warm than the SET 300B sound, but more incisive and detailed. And louder than you or your neigbors would want to hear, most of the time.
To address the LS3/5A's lack of deep bass, both Rogers and Spendor systems are supplemented by passive subwoofers driven by hefty transistor amps (Adcom and NAD), with active crossovers (Dahlquist and Paradigm) splitting the signal before the amps.
I would try the Little Dot amp with LS3/5A's. I think you will be plesantly surprised.
