As the people above say, you just have to have the LMIA supported job at the time of application, i.e. when you send your full application after you've received an ITA.
As someone with 3 months left on your permit you're by no means an unusual case.
Important things to consider:
Make sure you follow everything to the letter. Include every document. Triple check everything you send. Ask advice if you're in any doubts about anything. Make sure your employer gives you all the documentation you need using exactly the words needed.
3 months seems like limited time but it's enough time to do what you need so don't rush like a crazy person, you've got this.
Again because this is SO important. You may only have one swing at this because if you get cancelled down the line, you may not have an LMIA job any more. TAKE YOUR TIME and make sure you send EVERYTHING YOU NEED. Make sure it's all clear.
And hey, get someone else to sanity check your application before you send it... trust me on this, I had a schedule A request and included a stupid mistake which could have basically resulted in me getting cancelled (thankfully it didn't) so triple, quadruple check and get someone you trust to check it all again for you! It's by far most important you get this RIGHT than get it done quickly, you have time to get it done right!
And finally, move quickly, the quicker you start the more room for error you have. You're presumably going to need police checks from everywhere you've lived 6+ months... that can take time depending on where you get them from. While you're waiting for those police checks you can be double and triple checking all your documents and applications!
Good luck!
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