I am using a bought 100% lemon juice (pasteurized). I thought that it will be cheaper to squeeze some lemons and heat at on the stove for pasteurizing. How much time can I use my own pasteurized lemon juice? are there other health consideration I need to take into account?
Just because industrial food producers can create a safe process for a given preservation method, it does not mean that you can do it too.
The best you can do in this case is to make canned juice, which, as long as it is in a closed jar or bottle, will last on the shelf for months and years. But as soon as you open it, you will only have 3-5 days in the fridge, after which you have to throw out that can. You also have to subject it to proper canning temperatures for a sufficiently long time, so it will not taste like fresh juice afterwards. Also, it is highly unlikely that you will see any savings - even if your own time costs nothing to you, fresh lemons are more expensive than bottled juice.
Most people do not see the point in that and simply squeeze their lemons whenever they need juice. But if you want to go the canned route, you can simply follow any recipe for high-acid juice canning. And obviously, you don't need to acidify it extra the way it is done with other juices, since lemon juice is already more acidic than standard acidifiers like vinegar.
What my family does with the lemons from their tree is:
The squeeze the lemons and use either ice-cube trays or bags and just freeze the juice.
Then when they need some lemon juice the just take as many cubes as they need from the freezer, defrost and use it. According to this site the shelf life of the frozen juice should be about 3-4 months but my families experience is that it keeps well beyond that.