Hi Gareth,
This might be better in the CRM forum but here's my thoughts anyway.
You have to start by asking him if he thinks it's safe to continue. If he says yes then you have to state that you are concerned that it is not safe. He may well be able to explain why he considers it is safe and his greater experience may well support that argument. Certainly looked to me like an approach that should have been abandoned way before the rain hit! With an active thunderstorm like that over the airport I can see no justification for continuing the approach. So, how to deal with a Captain who insists on continuing.
In most companies I have worked for there is a statement in the Ops Manual prohibiting landing or take off in an active thunderstorm; if your company has such a rule that I'd remind the captain of it. That might work. If he still insists then you have to make a positive (but non threatening) statement to tell him that you do not consider the approach to be safe and that you would strongly recommend a delay until the storm is passed or diversion to the alternate.
If still no change then you are really in trouble and you have to make a more positive statement. Perhaps something like this "Captain, the thunderstorm and lightning over the airport are creating a dangerous situation and we must not go any closer".
If he still refuses to acknowledge your concerns then you are in a world of hurt. It doesn't really matter what you say now because (at least in my mind) you are passing a point of no return. If you have to be more aggressive then one of the two of you is going to loose your job - that's fine because I don't want to be in an airline which supports a Captain making those sort of decisions. Taking control is always problematic because, if he won't listen to your concerns then he is not likely to react well to you taking control of the aircraft! I guess you just do what you can to get him to turn away from the storm but, there comes a point where the danger of arguing at low altitude over what to do and who has control will be a greater risk than continuing the approach. Once safely on the ground you then need to start a Safety report and be prepared to answer some very robust questions - should be no problem so long as you have behaved professionally and are right in accordance with the company procedures.
Then .... look for another place to work!