Should I have my Luxman R-115 repaired?

Luxman should not struggle with driving 105/3 if you properly service your receiver. Make sure you prepare your receiver by overhauling it completely. At least what should be done is replacement of main filter power supply caps, but if you know you have distortion, than you might want to step into complete rebuild of BOTH channels. Bare in mind I usually replace caps with larger capacitance. Today there's better availability to replace originals with larger value for larger current reserve thus giving new possibilities of receiver to drive heavier loads.

When I service, I inspect signal path of amp and preamp with speakers or headphones with loose unterminated  leads to define a proper "menu" of restoration.

In poweramp section I usually check for bad solder joints and if they are around power transistors, I'd replace all power transistors(fortunately power transistors are cheaper than power tubes:)). Another sign of necessary replacement of power transistors is dry heatsink compound. If you have one or both channels distorted, it's mostly in driving on preamp stages. 

I'm local to North Carolina Raleigh-Durham and I do not ship. My flat rate for your reference (if you're shopping for repair techs) is $160+ parts. Parts may run anywhere from $20 to $150 depending on availability and pricing. 
Be noted that sometimes I have to wait for parts few weeks before getting them even if ordered from highly reputable sites such as Mouser or Digikey.

I may be shopping for a tech but I'm at the very western tip of North Carolina, a long way from Raleigh.  I'm located 2 hours north of Atlanta; 2 hours west of Asheville; and 2 hours east of Chattanooga.  Or, as many say, 2 hours from anywhere.