Two very good responses. Usually, when excavating that close to and that far below an existing foundation, the foundation needs to be underpinned. With an existing mat foundation, it might be reasonable to use a stiff sheeting wall rather than underpinning. Usually installing tieback anchors beneath an adjacent building is not a problem but, if the property is owned by someone else, you will need their permission and a temporary underground easement. Usually, you can convince the owner that tiebacks are the best way of protecting their property.
If you are digging 12 to 14 feet below grade, 14' long soldier beams are probably too short. In general you should have at least 5 feet of soldier beam embedment below proposed subgrade for braced or tiedback soldier beams. Cantilevered soldier beams usually have embedment at least equal to the height of the wall.
I would not cantilever next to the building under the conditions you have described. I would try to use tieback anchors installed just below the bottom of the existing mat foundation. I would design for an area surcharge equal to the design bearing pressure under the mat. I would not be against using active earth pressure. A 10' to 14' high wall does not need to deflect much to develop active pressures. A sheeting wall this low with tiebacks will usually have minimal deflections, with most of the deflection occurring before the tiebackeds are installed. That's why you want to install the tiebacks just under the mat. However, for a wall this low, if tiedback, using at-rest pressures should not have a significant effect on the design.
I would install the soldier beams at a conservatively close spacing, maybe 5 to 6 feet on center. This way the lagging boards are short, and not too heavy even if they are 3 or 4 inch nominal thickness. You may want to drill in the soldier beams rather than drive them in order to reduce vibrations to the existing structure. If you drill in the soldier beams, after placing the soldier beam, you should completely fill the drill hole with lean concrete or flowable fill. You do not want any voids around the soldier beams or behind the lagging. Although I feel that treated lumber is used too often when not needed, you may want to use it along the existing building.
Make sure that someone does a preconstruction survey of the existing building and that the building is monitored for vertical and horizontal movements during construction.