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I don't know a definite answer to this, but given the government bonus is not actually interest received on savings nor is the bonus one of the other specified allowable source of non-employment income, I would guess the answer is likely to be no.
I doubt it. Essentially the bonus on the Lifetime ISA is effectively a return of the income tax that has been paid on the amount that was invested in the Lifetime ISA. As it is a return of the income tax, that amount would have been included in your gross earnings/salary.