You shouldn't be having a problem with bubbles in lining paper. If you are it means that you didn't hang it correctly in the first place, (one example) - you should have soaked it for a decent length of time. If it's bubbled before you've emulsioned it....then it's definitely been hung incorrectly.

Is it normal for lining paper to bubble when painting?

The main reason for bubbles is that the dec missed areas when he pasted, or didnt leave it long enough to soak. He should have seen the patches showing through the paper caused by the paint lifting and filled, any decent dec would know with each grade of lining paper what it covers and what prep needs doing.

Can you paint directly onto lining paper?

Can you paint over lining paper? Yes, you can. In fact, it's an excellent approach to use for achieving the beautifully smooth finish of a newly-plastered wall without having to go through the process of replastering. Of course, it will never be as good but if you can hide the seams well, you'll be close.