During lucid dreaming, we sometimes feel that it is a repetition of (or in someway related to) a previous dream, but when we wake up, we can't recollect the first instance of such a dream. Why is this so?
Disclaimer: My answer is about recurrent dreams. I don't have any immediate sources to consult on the continuation part (and there are less references to it in literature), but I'd be very surprised if it is any different.
Firstly, there are many of theories that support the notion of recurring dreams. I know not of a single one that (explicitly or even reasonably implicitly) rejects such thing.
On cognitive perception
Secondly, you talk about perception, which in cognitive terms equates conscious access (rather than sensing in everyday language). So if you can (consciously) perceive it, it must be a genuine mental process that made it available (with the sole exception below).
Subjective reports = objective measurements
Thirdly, recurring dreams have been reported and studied for decades (in your case I'd probably start with ). Most of dream science is natively based on subjective reports. But recently, scientists have shown that monitored brain activity is in agreement with, and can even predict, those subjective reports .
So we really have all reasons to believe that what we perceive as a dream is what we actually dream.
The one exception for this, and it is my own informed suspicion, is that we may still have a Déjà vu (déjâ rêvé, in the question context) while dreaming - so it may be a false sensation after all. It is the same informed suspicion that tells me that if this happens at all, it should be extremely rare.
Sleep's low retention
As for the latter part of your question:
we can't recollect the first instance of such a dream. Why is this so?
If one is to make gross simplification, during sleep:
- Your long-term memory is 'not available' to remember stuff.
- Your short-term memory is even more volatile than it is while you're awake (there isn't central-executive process to exercise retention).
For the same reason, we often remember a dream just after waking up, but unless salient we fail to recall it shortly after.
 Zadra, Antonio, and D. C. Donderi. Nightmares and bad dreams: their prevalence and relationship to well-being. Journal of abnormal psychology 109.2 (2000): 273.
 Horikawa, Tomoyasu, et al. Neural decoding of visual imagery during sleep. Science 340.6132 (2013): 639-642.