If you are the middle proxy hop runner, Bob needs to know your pubkey and Lisa's payment hash. And you need to know Lisa's pubkey and payment hash that either Lisa or Bob share to you.

For Lisa to receive a payment from Bob without revealing her pubkey to him, she would be the one wrapping the invoice.

If Bob is using a custodial service and want's to hide that he is paying to Lisa, then he could wrap Lisa's invoice to hide her pubkey from the custodial platform.

If you are a middle proxy hop runner, you reveal your pubkey whenever you wrap an invoice for someone. There's no other way for the wrapped invoice to be paid otherwise. At least not without BOLT12 which would remove the need for a proxy completely.

lightning

The Rack - Manually stretch your lightning network payments

supratic

So if I understand correct, the hops are added at the beginning. Bob wants to pay Lisa privately. Lisa generates an invoice which Bob pastes into rack. Bob pick out your node to initiate more hops and another invoice is generated.

At this point is my node exposed to Bob?