Can I make apricot jam with just sugar and lemon juice?

you'll need apricots

yes, those will serve as your preservatives, but you will want to make sure that you can create a vacuum seal in order to kerp it for any reasonable length of time.

Try getting some glass bottles and metal lids for them; boil soke water in a pan at ~ 1/2 the height of the bottle, suspending it on a wire mesh above the bottom of the pan to prevent it from breaking. Wait a few minutes for the jam to heat up and then seal it. As it cools, you will get a vacuum seal.

Your apricot-sugar-lemon juice jam will be delicious, but fairly liquidy - a preserve. If you want it to sit up on your toast, or stay put in a sandwich, you need pectin. You can buy that in the grocery store; one brand name is SureJell and there's another prominent one too. The package will tell you how to use it.