Agreed. LT is defined as a function of intensity (power). Increasing lactate threshold means you are increasing the power for a given lactate level. Doesn't have anything to do with HR though.

People use Power, RPE and HR to estimate their LT. I prefer to RPE or power to HR but you can use whatever works.

The actual HR where LT occurs can vary depending on numerous factors including hydration, temperature, race jitters etc so trying to precisely determine HR at LT is not really necessary or possible.