Yes you should ask if you can join her in the lane.

The truth is I've never seen anyone says no when you ask.

Also you can join a lane with 2 people. Usually if two people share a lane, the two can choose between splite the sides and going in circle (for example, every stays on the right hand side and goes in order). If more than 2 people in one lane, everyone has to go in circle and keep a good distance. If you go to a swim class where lots of people are training together, it is not uncommon there are 3 to 4 people in one lane.