The question of who caused the delay isn't the issue, it is who provides the service. If it is LH and deicing happens to be a function which LH outsources, then yes, you have a valid claim unless there is some extraordinary circumstance as to why the deicing equipment was delayed. If this is an airport service, than you are out-of-luck as the delay isn't caused in the least bit by LH and it's not a question of the weather vs. non-functioning engine and so on.

This varies from carrier-to-carrier and airport-to-airport.