I suspect that when you think your father is being sneaky or lying to you, he is actually attempting to cope with his confusion. The early stages of Alzheimer's and
other dementias often keep a person in turmoil. He's aware of his slipping memory and tries desperately to hold on. Sometimes he may seek an explanation for his own peace of mind, but to you this may sound like a lie.
Every case of dementia is unique. For some people, the decline is pretty steady, while others experience a great deal of fluctuation. One day they will appear "normal," the next they may not recognize even the most familiar. This can be most disconcerting to family members. An otherwise loving wife may suddenly think her husband of forty years is a dangerous intruder and try to chase him out of the house with a frying pan. There's also no predicting which "memory" will surface at any particular moment. Your father remembered a brand new store, while completely forgetting something that you reasonably considered totally familiar, so when he gave you some crazy explanation, it's understandable that you would think that he was trying to fool you.
One of my acquaintances told me how she came to terms with her Alzheimer's. She had long been aware of her slipping memory and increased confusion, but she could not face the thought of this being Alzheimer's, so she had done her best to cover up and find excuses for herself, which had led to much friction within the family and alienation from her daughter.
When I met her two years after she'd moved to an assisted living, she related what had been her "wake-up call." She was driving her regular route back to her home of eight years, when suddenly nothing on her street looked familiar. Feeling that her brain had frozen, she had stopped the car cold in the middle of the street to try to get her bearings. She was absolutely terrified. Fortunately a neighbor saw her and managed to get her back home. She gave up driving that day, called her daughter and admitted that she did indeed need help.
Your father needs your strength and support. I suggest that you assume that he's not trying to deceive you, but rather that it's the disease surfacing. If you start with this assumption, you'll likely find that he'll start to trust you enough to share his fears and feelings with you. It will make life easier for both of you.