My take on this is that Sanji is indeed using the same powers as the Lunarians, but it has nothing to do with having Lunarian DNA or anything of sorts.
I believe what's going on here is same as Koala or Robin using Fishman Karate
Before Koala, we did not know that humans could use Fishman Karate, and most asumed that it's unique to the Fishmen, but that's proven to not be true. What the Fishmen have is the knowledge on how to use it, and it's something they'd share with very few non fishmen.
I believe the same is the case with the Lunarians. Their ability to create and control fire is one taught among them, and mastered through training.
I think one of the requirements to make use of these powers however was revealed by Oda in an SBS
and it has to do with a "heart that burns hot". Wether it's one of the base principles required to create the fire, or a requirement to prevent self harm from it's usage, i think it's something Sanji stumbled upon by himself because of his strong emotions, and ever since he has been using a raw form of Luarnian Fire abilities.
I'm also speculating that King's attire as well as his reserved behavior have to do with his fire powers.
For the first, my speculation is that King has burns on his body, because at some point he was forced to use more fire power than he can do safely.
The second, is that King controls his emotions, because otherwise he'd be at risk of using his fire powers recklesly.
The first and second also can tie into eachother, and it could be the case that at some point King's emotional state reached such heights that he ignited himself with such heat that it caused him those burns, and my speculation here would be that it has to do with the eradication of his people.
Now to go further into Sanji and his future development, i believe he is provided with unique tools that will eventually allow him to use greater fire powers than the average Lunarian.
Those tools are the fire resistance provided by his modified body, as well as the Raid Suit on top of his "burning heart".
With these Sanji will eventually be able to use safely flames that reach levels of heat like none could before him.
And naturally this also ties into what makes Sanji by far the best among the Germa siblings, because in spite of how well the fire powers and the Germa double layer of fire resistance complement eachother, without the emotions and the "burning heart", they are gated entirely from using these abilities.
I believe what's going on here is same as Koala or Robin using Fishman Karate

Before Koala, we did not know that humans could use Fishman Karate, and most asumed that it's unique to the Fishmen, but that's proven to not be true. What the Fishmen have is the knowledge on how to use it, and it's something they'd share with very few non fishmen.
I believe the same is the case with the Lunarians. Their ability to create and control fire is one taught among them, and mastered through training.
I think one of the requirements to make use of these powers however was revealed by Oda in an SBS

and it has to do with a "heart that burns hot". Wether it's one of the base principles required to create the fire, or a requirement to prevent self harm from it's usage, i think it's something Sanji stumbled upon by himself because of his strong emotions, and ever since he has been using a raw form of Luarnian Fire abilities.
I'm also speculating that King's attire as well as his reserved behavior have to do with his fire powers.
For the first, my speculation is that King has burns on his body, because at some point he was forced to use more fire power than he can do safely.
The second, is that King controls his emotions, because otherwise he'd be at risk of using his fire powers recklesly.
The first and second also can tie into eachother, and it could be the case that at some point King's emotional state reached such heights that he ignited himself with such heat that it caused him those burns, and my speculation here would be that it has to do with the eradication of his people.
Now to go further into Sanji and his future development, i believe he is provided with unique tools that will eventually allow him to use greater fire powers than the average Lunarian.
Those tools are the fire resistance provided by his modified body, as well as the Raid Suit on top of his "burning heart".
With these Sanji will eventually be able to use safely flames that reach levels of heat like none could before him.
And naturally this also ties into what makes Sanji by far the best among the Germa siblings, because in spite of how well the fire powers and the Germa double layer of fire resistance complement eachother, without the emotions and the "burning heart", they are gated entirely from using these abilities.