I know a couple who cleaned as thoroughly as possible with coarse tools and then washed the brick wall with hydrochloric acid. It neutralizes the alkaline mortar. They did it in several rounds and then with water a couple of rounds. Now they have a very nice brick wall. 
The mortar that was on the stones themselves, not the joints, came off much easier and the stones revealed their fine red shine. The mortar can almost lie like a dust on the stones. It did take off about a millimeter on the joint as well, but nothing that was directly visible.
Hydrochloric acid is not actually used for neutralization purposes. The hydrochloric acid dissolves the lime and removes the white lime film from the brick surface. It also dissolves the mortar. You should thoroughly wet the joints with water before you start brushing on the acid so the joints don't absorb too much of the acid. Afterwards, you should rinse thoroughly with water to remove remnants of the hydrochloric acid from the wall. Hydrochloric acid should be diluted. I read somewhere that a 10% solution is used to remove cement skin, so this solution should be sufficient to handle lime deposits as well. Start cleaning bit by bit from the top down. If you take on too large an area at once, it might be too stressful to manage rinsing off the acid in time. If it bubbles in the joints = the lime in the mortar is being destroyed, resulting in just sand falling out and the joints becoming too deep. Rubber gloves and safety goggles are a must.
You can achieve the same result with Kalkbort, but it foams like soap and can be a bit tricky to handle - it takes longer but is worth trying. Good luck.
gaia
You can achieve the same result with Kalkbort, but it foams like soap and can be a bit tricky to handle - it takes longer but is worth trying. Good luck.
gaia