Assuming this is a narrowband oxygen sensor:
Cold reading above 1 volt may be a little rich on warm up, but not unusual.
In closed loop the sensor should switch continuously between 0.1 and 0.8 volt.
When idling at least 2 times a second, the higher the rpm, the faster is should switch.
0.06 volt is very, very, very lean!
On boost it should be rich (high signal), but maybe 1.2 volt is just a little too much.

What do you want to achieve with attaching this sensor to the turbo timer?
What car are we talking about?