High voltage non-inverting operational amplifier for DC signal
You need some way of shifting the input signal to the new ground level. The easiest way is to use an isolation amplifier. How practical that is depends on any accuracy and cost constraints you may have and whether you can produce a supply rail relative to the Vee (you could always use an isolated DC-DC converter. There are probably commercial modules that will do this all in one. 

Alternatively you could make an analog level shifter by building a current sink that produces a current proportional to the 0-4V signal, and then receiving that at the other end. The LT6090 does not have an input common-mode range that extends down to the negative rail so it might make sense to create a pseudo signal ground at Vee+4V or so, and then you just need a resistor (for safety) to the current sink collector or drain and a feedback resistor (just build a simple inverting transimpedance amplifier). For example: 







simulate this circuit &ndash; Schematic created using CircuitLab

As shown this will yield a nominal output of 105V to 240V for input 0-3.86V.