Why must we assume that it was ice that did provoque an unreliable Airpseed situation.
Because it has happened before. Try checking the reason behind the 2002 Airworthiness Directive and the more recent focus on upgraded Pitot Probes that had not yet been fitted to the accident aircraft.
Lightning damage to radomes is very, very common and the results are not dramatic. Just a series of small holes in the paintwork.