Yes: there is אֹ֫כֶל 'okhel, probably the most generic term since it comes from אכל '-k-l "to eat".
Between lekhem and 'okhel, I expect the main difference is no more than that lekhem can mean bread if desired, and often does. In any case, lehkem certainly is general enough a term for "food" that we can see it in a doublet in 1 Kings 21:4, for example:
וַיִּשְׁכַּב֙ עַל־מִטָּת֔וֹ וַיַּסֵּ֥ב אֶת־פָּנָ֖יו וְלֹֽא־אָ֥כַל לָֽחֶם
[Ahab] lay on his bed, turned his face [to the pillow?] and did not 'akhal any lekhem.
Sometimes the meaning of lekhem is ambiguous. For example, in Genesis 18, Abraham says he'll get the visitors a smidgen of lekhem (פַת־לֶחֶם), but then kills a choice calf and brings meat, curds, and milk. He hospitably over-delivers on the promise, that's clear; but was his promise for food (surprise of quantity) or for bread (surprise of dish as well)? Maybe the guests didn't know any more than we do. But in either case, he didn't tell them he was serving veal. :)
There's also the seemingly rare מָזוֹן mazon, from זוּן z-w-n "to feed". One intuitive reason this would be rare is that Hebrew prefers to apply causative binyanim to verbs like '-k-l (cause to eat → feed).
If others have more detailed analyses, I'll add them (or they can free to write another answer).