The role of the FRO (which is short for the provincial government’s “Family Responsibility Office”) is to collect, distribute, and enforce child and spousal support payments. If your Ex has been formally ordered by the Ontario court to pay child or spousal support, then the support order is automatically filed with the FRO – your current lawyer will not be able to prevent that order from being filed.
However, if you and your Ex have not obtained a court order, but have instead entered into a domestic contract (e.g. a separation agreement) that satisfactorily addresses your support issues and you choose not to file that contract with the court, then it is possible to circumvent the involvement of FRO.
You and your lawyer would only want to do this if your Ex is making the required support payments and can be relied on to keep doing so. (But if your Ex defaults on the payments to a significant extent, then you can still file your domestic contract with FRO and enlist its enforcement assistance as usual.)