I doubt it is the lead. The audio data is embedded in the video data. Would be a very clever lead indeed that could strip out just the audio and leave the video intact.
Much more likely is the Blu-Ray is outputting a format the TV doesn't understand. LPCM is an alternative name for Stereo PCM. And plugging it into a socket that could be used with a PC is a possibility. Most TV's I've seen that have an HDMI plus 3.5mm jack for audio will have a setting to switch the audio between the HDMI and jack if they don't do it by auto detecting a jack plug in the socket.
And of course it is always possible there is some odd fault on the HDMI socket on the telly so always try another socket. And if you can try some other device with HDMI output in place of the Blu-Ray to see if that provides sound to the TV.