Can a properly summoned monster, that was returned to the hand, be discarded to the graveyard and special summoned from there?
Short answer: In this specific scenario you mention (back to hand) you can't.



Longer answer: Lets see some of the card text of BLS:


  Cannot be Normal Summoned/Set. 


This card cannot be normal summoned or set. 


  Must first be Special Summoned (from your hand) by banishing 1 LIGHT and 1 DARK monster from your Graveyard.


emphasis mine

The key part here is the "first" in the text. This means that you first have to summon it in the required way but after doing that you can Special Summon it by other means. This is the case for all cards that say the "must first be...", unless otherwise indicated.

Also, as Compulsory Evacuation Device does not negate the summoning then your BLS was indeed successfully summoned by the required way; if the case where that you opponent negated the summoning by any means (like with Solemn Warning), then you will not be able to bring him from the GY.

However, this case is a bit different as per the effect of Compulsory Evacuation Device. These type of cards are referred as Special Summon-only monsters (or semi-nomi). And yes you could bring your BLS back after succesfully summoning him, but that only lasts while it's on the field (from that link):


  After being properly Special Summoned, as long as that Monster Card remains on the field (even if face-down), in the Graveyard, or banished, it is considered properly Special Summoned.


So this means that you did successfully summon BLS... but it was immediately returned to your hand, where it's condition "resets"; you will now have to banish two more monsters to summon again.1



On the other hand, other cards like Blue-Eyes Twin Burst Dragon, are not able to do this, as they specifically restrict the summon to certain way:


  Must be either Fusion Summoned, or Special Summoned by sending the above monsters you control to the Graveyard (in which case you do not use "Polymerization"), and cannot be Special Summoned by other ways.




1 This "resetting" thing if I am not mistaken is not rare on other card games. In Legend of the Five Rings (RIP) this was the case when cards returned to hand, and my vague MTG knowledge says that this is also true there. 

Think of it this way: when that cards returns to your hand/deck, it is no longer public knowledge which specific card that copy was. There is no way to officially take track of what physical copy it was, nor tell apart from possible multiple copies in your hand, etc..