Thanks for all the responses. Do you think an orphaned girl who received an inheritance upon her 16th birthday would be legally allowed to rent an apartment if her lawyer volunteered to co-sign for her?
If your story is modern, not set back in history, then to receive an inheritance directly (as opposed to in trust), she would probably have to be the legal age of majority (whatever that is in her province), or else be an emancipated minor (which requires a court hearing). Inheritances for minors--at least, high-value inheritances like money, stocks, houses, etc.--are pretty much always in trust, i.e., the inheritance itself is watched over by an adult trustee for the minor's benefit. Often the instrument (will/trust document/whatever) will say who is to be trustee, and who is to take over if that trustee can't/won't serve; if not, the court will appoint one (her lawyer might be a good candidate for that).
If the inheritance can produce income (e.g. if the house is rented out, or the money is earning interest), often the
income will go to the minor, but the principal will remain in trust until the child reaches some designated age (like 18--have you seen the headlines about how the actor who plays Harry Potter just turned 18 and became able to access the $20 million he's earned in the Harry Potter movies? Until now, it was held in trust for him). The person leaving the inheritance can designate any age they want, though--21, 25 or even 30 are not uncommon; the point of that is to make the kid unable to directly access the money until he or she has grown up a bit. Most trusts usually also allow money to be taken out--not by the child, but by the trustee, for the child--for certain important expenses, e.g. medical care, education, or emergencies; it could also be set up to allow payments for her housing costs.
For the inheritance to go directly to a 16-year-old, I would guess that (1) she would have to be an emancipated minor and (2) the trust instrument would have to say she gets it "when she reaches legal majority" or something like that, i.e., it would have to NOT say an exact age. It wouldn't say "16," for the reasons above and more; and for the purposes of your story, it couldn't say "18" or older. But if it just said legal majority, she'd have a good argument, once she was legally emancipated, that she should get the money now. And even if she didn't get all the money now, if she got the income from it that might still work for your story; maybe the trust is set up so she can't access the principal (i.e. the actual big pile of money) until she's 18 or whenever, but starting at 16 she gets quarterly payments of all the income (e.g., all the interest on the huge pile of money, or all the dividends from the stocks or whatever). She could certainly do that while still a minor. Maybe until she was 16 the income was re-invested into the trust, not paid to her, but at 16 the payments would start being made to her?
As for the apartment, minors can't sign contracts--or that is, they can, but the minor can renege on the contract without any consequences, so people generally won't sign contracts with minors unless there's an adult co-signer or guarantor. But an emancipated minor is different. Also, even if she were an unemancipated minor, if the trust were set up to allow this, the trust itself could rent an apartment for her, with the trustee (maybe this would be her lawyer?) signing the contracts, and the rent being paid out of the trust. Or, as you suggest, the lawyer could co-sign, though I'm not sure why a lawyer would do that--why he'd make himself liable for her rent. Most likely he'd have the trust do it (if he were the trustee he could do this himself; if someone else were, he could ask them to).