How to distinguish real memories from fake memories during a lucid?

Recently I became lucid during a dream where I was coming back home from work. Everything was fine until I wondered if all I remember was just a dream or it really happened? I lost the dream because of I wasn't able to determine whether I dreamed that work day or it was for real. At the end, I woke up out of place and it took me a little to realize that I was taking a nap after work.
Do you have any suggestions on how to determine real memories during a lucid without forcing yourself to wake up when something like that happens?

Good question. I hope someone will have an answer, lol.

I have had lucids, in which I KNEW that events are real, that the apartment I am in is mine, and similar false memories. Maybe it's like this in low awareness dreams. When our memory is enough to tell us that we are dreaming, but not enough to help us distinguish truth from dream scene.

There is no quick answer. It is a matter of training (darn it, time and effort again?). You start with very limited goals as far as recovering waking memory and understanding. The brain eventually can do this and the confusion goes away. That is, with a lot of training. The first step is simply to address the fact that when you know you are dreaming, you must also be able to realize this means you are sleeping. Become lucid, then pause and reflect on the odea that you are clearly sleeping somewhere. After that is clear in your LDs, move to attempting to remember what phase of your life is currently taking place IRL. I mean simply are you in your twenties? Are you still in college, and so on. When that is now a part of your standard lucid experience you then do all of that and narrow your focus to "where is my body located?" That step is very hard, but after that you will gain by leaps and bounds. After many years of this training you can bring almost full waking memory into some of your better LDs. I can often know that it must be such and such a time of morning and that my wife has left for work, and that the alarm will go off soon as I have a Dr's appointment at 10 am.
I wish I could give an easier answer, but I do not know a short cut.

I really appreciate your answers!!

From previous experiences, I found it a little bit tricky by the time I got lucid and started to think that I was sleeping somewhere, because of most of the times I got too conscious of it and consequently woke up. This time, it wasn't funny to think that perhaps I was happily lucid dreaming in stead of going to work.

One more thing I noticed, there was a sort of mental block that didn't allow me to access my most recent memories, I don't know yet how is it going to be, due to I never attempted to consciously work on it, although I think it's good to have some sort of plan in order to achieve this goal.

I hope one day I will be able to recall things from my WL the way @Sivason describes, it would be awsome... and very useful!!

Thanks a lot!