I hear that the LimeSDR supports MIMO. I also hear that TX and RX must be within 61 MHz of each other. Does that mean there is one oscillator for RX and TX and that it is possible to do a coherent passive radar setup using the multiple RX feature?
No they don't. Unfortunately. That's why you cannot receive at two different frequencies (further apart than DDC can do).
Although there are two LOs (one for TX and one for RX) there is no way to configure LO_RX for RX1 and LO_TX for RX2.
You can however use one LO for both 2xRX and 2xTX for full coherency. AFAIK only problem for now is ADC ambiguity.