When you initiate a transaction you have two options.  You can either use the localbitcoins "transaction service" or you can agree to have the bitcoins sent directly to a bitcoin address.

If you choose to have bitcoins sent directly to a bitcoin address, then when you meet you can negotiate any exchange rate you want.  Then cash and bitcoins are exchanged.  There is nothing preventing adjustments to the exchange rate until after cash and bitcoins are exchanged and you each go your separate ways.

If you choose to use the "transaction service", then the localbitcoins contact page specifies an exact amount of bitcoins for the transaction, but the two parties  can still negotiate how much cash will be exchanged for those bitcoins.

If the parties wish to negotiate a differing amount of bitcoins to be exchanged, it is very easy to just cancel the current contact and create a new contact for a new quantity of bitcoins.