Fee negotiations in Lightning How are fees negotiated in multi-hop payments in Lightning?

Imagine a four-hop payment: Alice -- Bob -- Charlie -- Dave. Bob and Charlie advertise fees of 100 sat each, Alice thinks it's reasonable and starts routing the payment through this route. Does Bob know which part of the expected payment is intended to be a fee? What is Bob forwards the payment to Charlie taking 120, 150, or 200 sat instead of 100 -- what does Charlie do?

Is there anything that prevents intermediary nodes from lying about their fees?
The situation you describe cannot happen / would lead to a routing failure. I have created an 11 minute video explaining how htlcs are used in onion routing. Parts of the video (rather at the end) explain how fees are encoded within the sent onion. I think watching that video is the quickest way to understand the fee model of the lightning network. 

A tl;dw (too long didn't watch) answer looks like that:

If a node decides to maliciously collect a larger fee and forward the onion. The next hop will not be able to collect the fee as it advertised and will fail the routing process. In your setting this means charlie decrypts his onion and sees which amount to forward and sees from the incoming htlc that it would only receive a fee of 80 / 50 or 0 Satoshi instead of the advertised 100. As said charlie would fail the onion but not be able to blame Bob. Actually obs behavior would confuse Alice as she chose the correct fees. Alice could assume Bob was a bad routing node and elect a different part. However this mechanism is as far as I know not implemented yet.