So then the reverse could be true as well: If Brexit FAILS (GOD forbid), then a newly elected Parliament could vote to LEAVE and ignore the results of the vote, no?
Again, theoretically, yes. Brexit could occur by an Act of Parliament, but, again, ignoring a Referendum result would trigger a constitutional crisis and cause the intervention of the Queen.
If a government specifically campaigned on a policy of leaving the EU and won an election based on that campaign, that would be different - in that case, the election would be considered a de facto referendum in its own right.
Given what "naturalman",who certainly appears to be quite familiar with Parliamentary procedures and traditions,has said that,too,might be possible...but highly unlikely.He mentions that,if push came to shove,the Queen has the power to see to it that the results would be honored...and would use that power.