Not fully, and usually in only uncommon circumstances.
First of all, no matter which of you wants the divorce more – and even if you don’t want it to happen at all – you cannot try to force your Ex to pay for your lawyer merely by demanding it.
However, the Ontario Family Law Rules gives the court the power to deal with who pays for the costs of case, motion, appeal or enforcement proceeding. There is also a presumption that the “successful party” is entitled to his or her costs, but in Family Law cases the success is usually divided or mixed; this means each of you typically remains responsible to pay your own legal costs, including your lawyer’s fees.
With that said, there are special Rules to deal with costs where your Ex is the “successful” party in the litigation, but has shown outright bad faith, or has behaved unreasonably (e.g. withheld information, has brought fruitless motions, refused reasonable offers to settle, or has otherwise caused unneeded delay and expense). In these kinds of cases a court may order your Ex to pay some of your legal costs on a stipulated scale, but as a practical matter this will still not cover your entire lawyer’s bill from start-to-finish.