I've got an LG 42LH4010 TV - had it since new, bought it soe years back...
From what I can find online, looks like it came out around 2011.
I'm using Hass.io and a Broadlink RM pro to send the discrete codes, and I do have some of them working (HDMI3, HDMI1 etc).
Hass.io requies the Hex codes to be encoded to Base64 - which I've done.
However, the codes that work (that were included as examples) all start with "J", the Hex codes I've found for the LG - when encoded into Base64 - all start with "AA".
More details on Hass.io & Broadlink integration here... [Link: home-assistant.io]
For example, one of the codes I have working is...
Interestingly, I note the working codes (starting "J" - see link above) do actually have the "AA" after the 4-char prefix (in the above, after "JgBI").
Not on my Hass.io box to confirm, (I dont thinks it's a case of adding that prefix, as that prefix itself changes slightly between functions).