To answer this question you obviously need to have recognised that eutectic tin-lead solder melts at 183°C, some 34°C lower than your new lead-free material. If you didn’t get this far, then take a fresh look at Solder materials.
Given that temperature difference, one realises instinctively that, whatever soldering process is to be used, the likelihood is that there will be a substantial increase in the maximum temperature to which the laminate is exposed during processing.
You should explain to your manager that, although the operating temperature for the circuit has not increased, materials with a higher glass transition temperature will be needed in order to withstand even short-term exposure to the soldering conditions. Failing to do this will result in a range of problems, from loss of adhesion of the foil, delamination of the structure, and loss of integrity of the plated through-holes.
It is probably important to point out that the changes made apply only to the resin within the laminate – the basic glass weave structure can be identical, but the resin needs to be compounded so that its glass transition temperature is higher. Typically, in the case where one is using standard FR-4, this means specifying an epoxy resin with higher functionality and more cross-linking.
If you haven’t already been asked, you should at this stage let your manager gently off the hook by explaining that the glass transition temperature is a phase transition that takes place within thermosets, above which all their physical properties change, and in particular the z-axis expansion of the laminate greatly increases.