Hey, so there's a professor on here who disagrees with this, but this is what worked for me so I'm posting anyways. Here is what UOttawa states: "The Personal Statement is a very important part of the application and should be written with care. You must also submit to OLSAS two letters of reference. While at least one reference must be from an academic source, it is preferable to have two academic references." Reading these instructions (very similar to my school), here's what I would do if I were you:
For your mandatory academic reference, it doesn't necessarily need to come from a professor. Are there any TAs that you could ask? What about an internship/co-op boss you had (if you did that in your undergrad)? You need to find someone who can attest to your academic work; it needn't be an actual professor. Disclaimer: This is Osgoode info. I do not attend UOttawa. Please confirm with UOttawa before that your 1 mandatory academic reference does not need to be from an actual professor before you file your application.
Then for the second letter, I wouldn't bother with beating a dead horse and trying to pull a second academic reference out of your ass. Have you worked before? Do you have an employer, present or previous that can write an astounding reference letter for you? If not, did you volunteer anywhere on a regular basis? Is there a volunteer coordinator or higher-up at the organization that can write an extraordinary letter for you?
Then just spend a lot of time on your personal statement. Have a couple current law students read it over if you can, so they can tell you if it's too sentimental/not sentimental enough.