The two men together contribute the funds to keep the Salvation Army shelter open.
The character of Lord Saxmundham is introduced in act 2 when Mrs. Baines says he has promised five thousand pounds to keep the shelter open. Barbara says she has never heard of him, and it turns out he is the distiller of Bodger’s Whisky, Sir Horace Bodger, making an unlikely savior. But according to Undershaft in act 2, he has already saved a cathedral and his party:
He is one of the greatest of our public benefactors. He restored the cathedral at Hakington. They made him a baronet for that. He gave half a million to the funds of his party: they made him a baron for that.
As no further reward would come for the five thousand, Undershaft expects it will be to save his soul. Undershaft then commits to putting up the remaining five thousand, to complete the ten thousand pounds needed. Barbara is initially horrified, as the money is coming from alcohol and armaments, but Mrs. Baines is more pragmatic:
Lord Saxmundham has a soul to be saved like any of us. If heaven has found the way to make a good use of his money, are we to set ourselves up against the answer to our prayers?