Your TV is adding the delay. Ways to resolve it:

• Switch to optical - TVs don’t usually delay that
• Use an HDFury to extract the audio instead of letting the TV do it
• Get a different TV

So I connect my HD recorder and Blu-ray player to my TV using HDMI cables and then connect my TV to the Beam using an optical Toslink cable via an optical to HDMI converter? Will this resolve the issue?

I don't know what an HDFury is so will have to check this out.

I'm not in the market for a different TV as I'm happy with my Panasonic TX-50DX750.

However, if I did upgrade to  Panasonic TX-55LZ980 would that solve the problem or would it be an expensive experiment?

I have had problems with lip sync from several televisions and I don’t think buying a new one would in any way guarantee a solution.  I have also had problems with optical, so I would not guarantee that either.  The only solution I have found for this is to avoid sending the audio through the TV.  For optical I used to do this with a cheap optical switch.  For my Arc I have an HDFury Arcana device.  This splits the HDMI input into two, sending the picture to the TV and the audio straight to the Arc.

The Arcana is pricey but works brilliantly.  It also gives me Dolby Atmos sound (which my TV is too old to handle).

There may be cheaper options than the Arcana now, but bear in mind that you need to feed your Arc or Beam an HDMI-ARC signal, not HDMI, so basic HDMI switches won’t work.  However, you might need an HDMI switch to bring multiple input devices down to one connection to the Arcana.

Exactly. It’s worth a try. Whether it actually works depends on whether your TV delays the audio optical path, which is unlikely but can happen.