However, I can’t seem to find an optical Bluetooth converter that states that the tv’s internal speakers can still be heard when the Bluetooth headphones are also being used.
You won't get any third-party device manufacturer to commit on the way a TV might work. They don't make the TVs, and they can possibly be expected to check on thousands of TV models to see if the TV will or won't do something. All they do is make a device that connects to an optical socket. It doesn't even have to be on a TV. As long as there's a stereo PCM signal then their device will turn that into a Bluetooth audio signal. That's about as much as you can expect really.
This is from the LG web site support pages for the 49SK8500PLA. I couldn't find a model match to your 49SK5800PLA, so I took the guess that this could be a typo with the 5 and 8.
Here I'm looking at the same user manual that is built into the TV. I think you have to press help on the remote or select from a main menu option to bring this up. The breadcrumb trail is Tour of Settings > Sound > Sound Out, and then I scrolled down to find this;
LG are saying that it is possible to use the internal speakers and optical, but they're vague about having more than two simultaneous outputs. This level of vagueness has been a growing problem with user manuals. The Web OS manuals aren't great, and it doesn't help that manufacturers try to cover lots of models with the same generic publication, so you find features described that your own TV model may not have. It's very frustrating from an installer's point of view.
The issue for you is two-fold.
1) Getting the TV speakers and Bluetooth on at the same time - but this may not be required if optical can be used instead
2) Finding out if optical works regardless of other settings
For #1 there could be a couple of reasons that prevent this. The simple one is a menu setting, but looking at the manual the only option appears to be Bluetooth output On or Off. This could indicate that the TV has only a single digital audio processing circuit, and it can either create audio for the speakers and wired headphones (both analogue) or be dedicated to creating audio for Bluetooth.
My own TV is a Panasonic. The Bluetooth connection gives me a choice of having BT only, or sound output to all the connections. In my case that's HDMI ARC, Optical, the TV speakers and BT. I realise that this doesn't directly help you with your TV. I'm simply highlighting that it's possible. Your mileage may vary.
Point #2 - My gut feeling is that optical will work when the TV speakers are running. There's a common issue when basic sound bars with optical in are used. It's that the TV speakers need to be turned down otherwise both play together. This is because both optical and the TV speakers work at the same time.
The only way for you to be satisfied on this though is to try it on your TV. That might mean borrowing a speaker with an optical input from a friend or family member.
Regarding lip sync, there are two things within the TV of which you need to be aware.
First, the TV audio settings: Every bit of picture processing creates a delay in the picture, and every bit of sound processing creates a delay in the sound. The basic picture controls such as brightness contrast colour and sharpness create negligible additional delay. More processor-intensive operations such as dynamic contrast, dynamic colour, dynamic tone-mapping, TruMotion, etc all have a more significant overhead. Gamers call this picture delay
Lag. For them, the issue is that the screen image is a fraction of a second later than the images the console is sending out, and that means their reactions are already late. They get shot, or they miss the apex of a turn. Most TVs now incorporate a minimal lag setting called Game Mode. This switches off a lot of the processing that causes the problem.
Sound can also be delayed but for a different reason. In the main it's the time taken to decode an audio signal to create a Dolby Digital (DD) audio output. That might seem a bit odd when HD TV channels and a lot of streaming claims to be DD5.1, but there is a difference between what is broadcast and what comes out of the digital audio connections on a telly. It's all to do with saving space during broadcasting or streaming.
They send the signal in a newer audio format called HE-AAC. If a Dolby Digital signal is required from the TV then the TV decodes the HE-AAC to create DD5.1. This takes time and it throws out the lip sync. This only applies to the HD channels from Freeview, and streaming. Changing the TV audio setting from Dolby / Bitstream / Digital to PCM Stereo / Stereo reduces the work the TV has to do, and so lip sync timing errors are reduced.
Pulling all of this together, it's possible then to have sync issues where the sound comes slightly after the picture, or the picture comes slightly after the sound. Your LG TV has lip sync adjustment. It's in the sound menus. Adding more delay to the audio is relatively easy as a process in the TV. It's far harder (read: 'impossible' in most cases) to add extra delay to the picture.
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