You didn’t say exactly which action your Lancaster rifle is based on?

Is it this one?
https://www.gunsinternational.com/guns-f...un_id=101100060

If so, be aware that the action was originally made and proofed for a black powder cartridge, likely no more than “10 Tons” working pressure in the British system.
The .375 Flanged 2 1/2 is/was14.5 Tons
The .405 in modern Kynamco loads is 16.5 Tons

Both of these “modern” smokeless loadings are close to what the original proof loads were for the rifle as it originally was.

Now, yes, it (maybe) had passed a new Nitro reproof in 1923 and it should be marked as such with appropriate London or Birmingham reproof marks.
BUT.....that just means it passed proof....it does not mean that continued shooting with .405 or even .375FL NE will not shoot it loose or eventually crack parts.
After all, despite wonderful design and engineering they are 1870’s/1880’s iron and steel.

Sorry to say but:
Were it my nice old rifle, if keeping the .405 barrel in place, I would only use loads equivalent to the old black powder pressures. In other words equivalent to the grand daddy of the .405 the black powder .40-72 Winchester, and you could use appropriate smokeless loads if need be.
Refit the .375 barrel? Then I would go with .38-72 Winchester equivalent loads.

If the rifle still has the Lancaster serial number visible you can use this to estimate the date:
https://www.doublegunshop.com/dgsnos3.htm

I’m sure some others will chime in with their opinions.

Please share some pictures!
-Mike