First off, I do not recommend lying to anyone. Besides being bad for your karma, it's also fraud to misrepresent product details to claim warranty service. I doubt it would help much, anyway.
Here are some things to consider. When you purchase anything with a warranty, the warranty starts from the date of sale. If you can't remember (or provide a receipt) the manufacturer will usually honor the warranty from the date of manufacture, which they can look up by lot and serial number.
According to the LG User's Manual:
2. The limited warranty extends only to the original purchaser of the product and is not assignable or transferable to any subsequent purchaser/end user.
3. This warranty is good only to the original purchaser of the product during the warranty period as long as it is in the U.S., including Alaska, Hawaii, U.S. Territories and Canada.
So, technically you are not entitled to warranty repair or replacement. That said, manufacturers are not evil greedy b*stards all the time. Give them a call and explain the situation. They might still fix it for you if you are polite and reasonable.
For additional support, contact LG Customer Service at 800-243-0000.
This is how I see the call going ... (After you've pressed 1, 6, 9, waited on hold for 15 minutes of irritating muzak, hung up and called back ...
Just kidding ... maybe ... i don't know how good or bad LG's support line is.)
LG: Hello, my name is Bob (in a thick accent), how may I help you.
You: I have a Nexus 5 phone that has developed a defect on the screen. The problem is, I don't have the original receipt.
From here it could go one of two ways ...
First way:
LG: That's okay, if you give me the serial number I can look that up for you.
Second Way ...
LG: I'm sorry, without the receipt we cannot provide warranty support.
In any case, then you'll know.
If you do get further with LG support, I doubt they will have a record of the original purchaser unless it's already been submitted for warranty work, but the date of manufacture could be past a year by now. In any case, it won't hurt to call and then you'll know.