Logic Level Converter not converting low logic level as expected?
If level converter works when you directly connect LV input to GND or 1.5V and does not work from DATA/CLK pins then it means logic levels on those outputs do not have enough swing to switch the FET. Or maybe do not have enough sink capability.

One possible workaround is to reduce pull-up strength on that adapter board from 10K to 22K or more (on LV side only).

However more reliable solution would be to use different level shifter, something that does not depend on Vgs of the MOSFET and has high input impedance. Like PCA9306 for example.