Since the question does not mention the particular grantha or context in which ‘auspicious lakshana’ is used, I can only explain a few possible meanings.
I would try to answer this question based on my limited knowledge. See, if you mean ‘auspicious lakshana’ as a divine presence in a blade of grass or an insect, then it may be done via methods like Abhimantrana. When we do Abhimantrana, we take the blade of grass, or akshata, chant the Mantra, and the particular devata sannidhana comes in that. This is possible. In the Ramayana, we hear the story of Kuranga, the demon. Indra’s son Jayanta had taken the form of a crow, and then Kuranga entered his eye.
He came flying in the sky and saw Sitadevi. He flew and tried to attack Sitadevi’s breast. At that time, Lord Rama woke up, took a blade of grass, and did Abhimantrana of Brahmastra in it, and threw it at that crow, and the crow went to Lord Brahma and Lord Shiva, but Lord Brahma and Lord Shiva refused to help, because they also couldn’t do anything in front of Rama’s arrow. Then finally the crow went to Vaikuntha and asked Srihari to rescue him. Srihari instructed him to go to Ramachandra, who is His own roopa, and ask forgiveness. There, Srihari, as Rama, will forgive him.
Similarly, the crow came there and begged forgiveness from Lord Rama. Lord Rama removed one eye of the crow, and Kuranga died. Rama warned Jayanta not to do that again and sent him back to svarga. So, in this way, the Abhimantrana works. If you see, the Swamigalu takes the mantrakshata in His hand and recites a mantra. So, during that time, the devata who is the mantra pratipaadya, or the one who is extolled by that mantra, puts His/Her presence in the mantrakshate and hence it helps us in removing our obstacles. So, in a way, by the presence of devatas also, even a small blade of grass has auspicious lakshana or devata sannidhana.
If you talk about an insect, then it may be that the svaroopa yogyata of that insect might be more. That insect may be a yogya jiva, which, due to a curse, may have attained that insect’s body. Because of that, it may have auspicious lakshana within it, because, if you see, a normal insect doesn’t possess all that. It is normal as we see. Lord Vedavyasa gave the whole kingdom to an insect to rule. It so happened that once, Lord Vedavyasa was coming on His way when He saw an insect.
Lord Vedavyasa knew about the insect (Because He is Supreme Lord Vishnu Himself, who knows the biodata of every soul in this universe, be it devata like Brahma, Vayu, and Rudra, or normal human beings, or the demons). So, Lord Vedavyasa asked the insect, “I will give you a human birth. You will rule this kingdom.” But the insect refused a human birth and demanded to rule the kingdom in its insect body. Lord Vedavyasa blessed it in that way, and after that, great kings came to the insect to pay taxes to it. This story comes from the story of Lord Vedavyasa.
So, it is possible in this way. Now, if you mean by ‘auspicious lakshana’ devata avesha, then it can certainly be possible for a devata to keep his/her sannidhana in a jiva. For example, the 16,108 queens of Krishna. Now, out of these 16,108 queens, Rukmini Devi and Satyabhama Devi are Saakshaat Lakshmidevi. And the remaining 16,106 queens had the avesha of Lakshmidevi, or the presence of Lakshmidevi within them. Out of those 16,106 queens too, Jambavati had the maximum sannidhana of Lakshmidevi within Her. So, like this, the devatas have the power to keep maximum, middle, or even lower sannidhana of them within a particular jiva.
Even if you observe devatas, humans, animals, birds, etc., then Bhagavan has His sannidhana in them too. Bhagavan is present in all the jivas, at all places. He is even present in the cleanest place, and even in the dirtiest place, because He is the ultimate support to everything that stands in this universe. But even in the dirtiest or inauspicious place, He is not affected by the inauspiciousness of that place, because He is always pure (Pavitraanaam Pavitram Yo Mangalaanaam cha Mangalam). But in inauspicious places, He doesn’t show much of His sannidhana. Whereas in an auspicious place, like a temple, Bhagavan shows His maximum presence.
But the thing is, as per the Svaroopa Yogyata of the jiva, and as per the jiva’s karma, Bhagavan’s sannidhana is more in the jiva. For example, Vayudevaru. He is equal to Brahmadeva. He is the most Saatvika Jiva and is Jivottama. So, Bhagavan has the maximum sannidhana in Brahma-Vayudevaru. As the hierarchy lowers, the sannidhana too lowers, but compared to humans, the sannidhana of Bhagavan is infinitely more in devatas. In humans too, within the saatvika jivas, Bhagavan has His maximum sannidhana. This doesn’t mean that the Rajasa or Tamasa jivas don’t have Bhagavad Sannidhana within them. Bhagavan is present in them too, but He doesn’t make us feel His sannidhana within them that much, as it is in the Saatvika people.
If you take animals, then inside the cow, Bhagavan has the maximum sannidhana. This doesn’t mean that He is not present within a dog, or a cat, or a lion. Yes, He is present in them too, but He doesn’t show His sannidhana within them to the extent that He shows His sannidhana in the cow. That’s why the cow is known as ‘Gaavah Vishvasya Maataram’ and is worshipped that much in the Sanatana Dharma. So, in this way too, Lakshana can be taken as the extent to which Bhagavan shows His presence in us, though He is present in us. And the Saakaara Bhagavan present within us is the same Bhagavan who is in the Ksheerasaagara or Vaikuntha, sleeping on the couch of Aadishesha, being served by Lakshmidevi. Remember, Bhagavan is within us, and we are not Bhagavan because we can never become Bhagavan, even after Moksha, and this is the Siddhanta of Jagadguru SriMadhvacharya.
I don’t know whether I cleared your doubt or not, because, I feel the question lacked some context needed to answer it more precisely. You could have elaborated the question a little more.😊
Hope it cleared your query!
Jay SriRam!
ShriKrishnarpanamastu!