I have soldered a copper plate to the inside of the lid, with a little thermal compound to bond to the chip, as shown in attached photo. Running the LimeSDR from HDSDR tuned to an FM radio station, I measured the following temperatures with an infra red thermometer underneath the LimeSDR. I measured underneath because the shiny metal lid gives a false reading on top of the Lime chip:
Lime chip 41.8 degC FPGA/USB i/f 45.4 deg C.
Previously, the Lime chip was at least as warm as the FPGA and USB i/f.