I keep a personal journal, and I would like to lock it.
There are several personal journals with locks on the market, but they are too expensive.
How can I lock a 5-subject ring notebook?
You don't say what you consider expensive, but a quick search shows quite few locking notebooks that fall under $20 and some of them are less than $10.
But if you're looking for a multi-use system (one that doesn't create an on-going expense when replacing each notebook), this notebook cover will allow you to lock up anything you put inside it.
Here's another with an integrated clipboard.
Apart from locking your notebook inside something you already have (e.g. a safe or locking filing cabinet), I can't imaging buying or even building something much cheaper.
Get a small padlock. Drill out or punch a hole through the notebook edge that is a bit bigger than the padlock's shank (the curving part, also called the shackle). You then can lock it at will. If you budget allows, two locks at the top and bottom corners will make the notebook almost impossible to peek into.
This method will work if you leave reasonable margins at the edge of your pages, but will not necessarily be completely secure; the journal could still be opened by ripping the lock out of the paper. However, it will certainly discourage casual browsing, and you will know if somebody has broken in.
Also, this is still likely to cost some money, but less than a special journal. Asking friends or family if they have a lock they aren't using could get you a free one. Luggage locks might be an ideal size.
It depends on how secure it needs to be, if very high security is needed you must keep it in a safe, however this is expensive. A chest with a padlock is the next option but is still probably out of budget.
If such security is overkill, use two pieces of plywood, sheet-metal or any other flat, strong material (can be scrap). Draw an outline of the notebook and use a large diameter drill to drill several holes in both pieces al around the outline. Thread the cable of a small bicycle lock through the holes all around the notebook.
Out of the box solution: Use google drive.