Will the Pb part handle 240C? That is the first question that you need to answer. If it will then yes I would run the pbfree paste and profile. I assume that all other components are pbfree. If not, the same questions will need be asked as for the BGA.
If it won't handle the increased temp:
When we are faced with this situation we use lead paste and profile. We also inform the customer that we will not warranty there product for any BGA failures due to the non-optimum reflow parameters that have to be used. We inform them that the structural integrity of the Pb free BGA will be compromised and they assume the risk.
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