Define "lobbying"; I'd say "Yes", but the vagary of that word shifted me to "Unsure". Also, good luck getting Britain and Israel to honor any such thing! This might be a nice test of whether the government's boundaries really match the country's.

Not banned, but closely controlled and backed by laws that make transgressions both personally and financially unacceptable. Ideally, foreign governments should interface with the US through diplomatic exchanges. But that typically does not include contacts with Congress or with state governments. However, the use of emoluments in these contacts should be strictly banned.

Foreign embassies already pay lobbyists to shape trade deals and defense contracts. If you say yes, does that include allies like Japan and the UK too, or just rivals?