If it is high quality imitation lobster and you are not amongst the highest skilled tasters (few of us are), you won't be able to tell the difference by yourself.
Imitation seafood is made from surimi, which is made from various whitefishes (most often Alaskan Pollock). The surimi is mechanically formed, colored and flavored to look like whatever species they are trying to duplicate. Sometimes the results are amazing. Behind the curtain, this is for crab, but I'm sure lobster is similar:
Handbook of Food Science, Vol 4: For the production of crabmeat analogs the Surimi paste containing the desired additives (with the exception of red colorants) is sheeted in a thin layer and then heat set. After this first heat set, the sheet is scored with the device that looks like a large comb. the sheet is not cut completely through. The scoring forms a long thin strips that resemble crab muscle fibers. Several of these strips are rolled together to form "muscle fiber bundles." These are set and then a portion of the outside surface is colored red with a blend of Surimi and food coloring. The ropes are then cut into logs (approximately 4 inches in length) or into small cylinders or diagonal cut product for salad chunks.
And if the cook lightly shreds the immitation crab, it's extremely hard to tell the difference.
I googled "detecting surimi" and learned that it is not an easy thing to do. There are people trying to do it with mass spectrometry and other complicated lab methods.
I'd say the lobster roll meat is one of:
- it's real (guessing from their reaction to your inquiry, unlikely)
- it's a high quality immitation lobster
- it's canned real lobster (I never tried it)
If you like the sandwich, consider keeping it in your routine.
(a timely question, a surplus of pollock/surimi is on the market, we'll see more of these surimi analogs)