Nope, it doesn't. The friend just needs to have invested at least £500 within 120 days of opening their new Dodl LISA, ISA or Pension. The cash for this invested can be added all at once, or in one go, including a transfer from another provider. Remember though, the first one-off payment to a Dodl account needs to be a minimum of £100.
Before the voucher codes are sent out, Team Dodl will do one final check to make sure the new account has invested is at least £500, otherwise the codes won't be sent (sorry!). Check the T&Cs for more details.