Op amp driving large capacitive load - do I need to be careful during power off?
Yes the opamp could be damaged in the situation where the supply voltage drops the voltage at the opamp's output. Usually the Absolute Maximum ratings forbid that the voltage on any pin rises more than 0.6 V (one forward diode voltage) above the positive supply rail pin's voltage. This is to prevent the ESD protection diode (between any pin and the positive supply rail) from conducting.
In the LTC6090's datasheet there is no such restriction but that doesn't mean it is OK to have Vout &gt; V+. Looking at the diagram on page 11 it appears that there is no ESD diode between OUT and V+ but it is possible it was simply not drawn.
What I would do is add some diodes to prevent getting a too large voltage difference between OUT and V+. I would do this:



simulate this circuit &ndash; Schematic created using CircuitLab
Diode D1 will start to conduct as soon as the +140 V rail drops below the voltage at the opamp's output. I have drawn 1N4007 but perhaps a Schottky diode would be more suitable as it has a lower forward voltage. Do use a diode with a reverse voltage larger than 200 V.