Yes, you could.
The drawback to this is you will need to pour the oils out of the jar when you make soap, and most of the jars are not ideal to use a spatula to scrape out most of the oil that will be left behind.
You do not want to make soap in a mason jar. Exposure to your lye will slowly etch the glass and make it brittle. Also glass in general is susceptible to thermal shock. Placing a warm jar on a cooler surface can make it shatter.
So you should not be mixing your lye in glass.
What I do us use paint mixing containers from a hardware store. They are the right plastic, you can buy lids for them, and they are very affordable.
I measure out 4 - 5 batches out at a time, put a sticker on the lid with my base oil (either lard or palm) and put the lid on. The fit in a small microwave fine when I need to melt them down, and they have a good sized opening so you can scrape to your hearts content.
These are what I use. Lids are another $1 or so.
http://www.homedepot.com/p/HDX-2-5-qt-Natural-Multi-Mix-Container-3-Pack-210216/204303497