I use 4 LR44 batteries (yes, 4) to get 6V. Stack it together, put some wrap around them and put it in.
Then with a small TO-92 size transistor, LM 317LZ, and 2 resistor, I made a simple 2.7V voltage regulator, and put it on the base area. There are enough space there to put the voltage regulator (don't forget to put some tape to prevent shorting). On mine, the red cable that connected to the metering circuit is the power source from the metering switch, so use that one as the source of regulator.
the regulator it self will regulate with 5mA current, but the best of Lynx is that light meter is not working if you don't press the switch, so 5mA for few second will not drain the battery too much.
I have tested on mine and the regulator work very nice. Unfortunately I have another problem that the resistor plate in aperture/speed ring is having intermitten contact. Too bad I can't use the regulator.
at the end, a small 20$ gossen pilot meter attached to the hotshoe solve my metering problem..ha..ha..