LM35 max temperature I read is 75C while thermocouple says 120
The LM35 is very simple to use, but there are still things you can do wrong. It is voltage-output so you are connecting to an amplifier (like an op-amp) output.

As such, putting excessive capacitance on the output can cause high-frequency oscillation, which you may read as a strange DC voltage.

See, for example, the datasheet figure :



The LM35 is not necessarily stable for >50pF loading, so if you have a long cable or a capacitor on the output, that is probably the cause of what you are seeing.