Agree. I have just discovered I can access the OED with my library card, so here are the definitions there (with abridged citations for 'lump').
sugar lump n.
1901 R. KiplingKim xii. 307
She chuckled like a contented parrot above the sugar lump.
1964 D. FrancisNerve ix. 122
The dope has been given to the horses on sugar lumps.
a. A compact mass of no particular shape; a shapeless piece or mass; often with implication of excessive size, protuberant outline, or clumsiness. Also ellipt., = lump of sugar.
1738 Swift Compl. Coll. Genteel Conversat. 95
She gives the Child a Lump of Sugar.
a1916 ‘Saki’Toys of Peace (1919) 24
Little friendly questions about weak or strong tea, how much, if any, sugar, milk, cream, and so forth. ‘Is it one lump? I forgot.’
1922 H. S. WalpoleCathedrali. v. 85
No, I'm afraid I don't—thank you, Mrs. Sampson. One lump, please.