My coach just walks up and down the strip giving me cues to hit. Is that really all a private lesson is?

That is the classic core of a fencing lesson, and yes, it is normal, especially in your first year or two of lessons. The coach moves up and down the strip controlling distance and gives you a cue, such as opening a target, extending, or taking your blade, and you respond with the right action at the right moment. It looks simple, but it is training technique, distance, timing and reaction all at once, and it gives the coach a close view to correct your hand position and footwork.

What should change over time is the cue, not the format. As you improve, cues should get smaller, faster and better hidden, the way real openings look in a bout. The coach should also start throwing false cues you are meant to ignore, so you stop jumping at every feint. Coaches describe lessons on a scale from technical to tactical. Technical lessons drill one action with lots of repetition. Tactical lessons have the coach build bout-like situations where you must read what is happening and choose. There are also short warm-up lessons at tournaments, built from familiar actions for confidence.

Beginners get mostly technical work, and a new coach will re-check your basics even if you are experienced. That is normal, not an insult. After a couple of years, though, you should see more choice, more open situations, and a clear link between the lesson and what is costing you touches. If every lesson is identical and your coach never watches you bout, raise it. A lesson with no progression at all is a fair reason to ask questions.

You can get more out of each lesson by treating it as a two-way conversation. Arrive warmed up. Tell your coach what went wrong at your last tournament or club night, and bring video if you have it. Ask what a drill is for, because knowing the purpose makes it stick. Afterward, write down the one or two things you worked on and try them in bouts that same week. Ask your coach to watch one of your bouts occasionally, since that is where lesson work either shows up or does not.