Thank you so much. I forgot to mention but I am a 3p female shooter and I'm not used to heavy rifles. I'll check out the ones you mentioned and I'll probably test some in person to see how they feel. Thanks again!
Yep, as above all the manufacturers offer lighter barrels for their top-end guns. Anschutz call theirs the 1907 (also a complete rifle, but available as just the barrel/action); FWB make a really light fluted barrel.
If you're looking at second hand rifles an Anschutz 1912 or 1914 would be ideal, as these combine the lighter 1907 barrel in a ladies size wood stock that's a bit lighter than the alu models, but still has lots of adjustment. Used Walther and FWB rifles are a less common in the UK, but a nearly new rifle with a light barrel would be great. Depending on your budget, a cheaper option would be an older rifle, like a UIT standard; these are only a little heavier than your LG400, although with a fairly basic stock, but if it's an Anschutz older barrels will drop straight into a new (or nearly new) stock.
Depending on where you live, having a gunsmith fit a lighter and/or shorter barrel to a used rifle, or shorten an existing barrel could be an option. Light aluminium extension tubes can bring the sight radius up to normal.