Getting contacted by an Infernal can have many reasons. If they reach out to you, there's always something they wish to deliver and it's best to listen and let them show what they have for you, especially if your intuition tells you to. It doesn't mean you must rush, but you better take notes and acknowledge their approach.
Infernals know us very well, they all have their 'strong suits', so they know when to step up and reveal themselves to us. The timing is never 'accidental' and by any means, not meaningless, so watch out. We are entering and leaving 'chapters' of our life, and by a door closed, opens up a new one. They know when it's their time to enter, when their 'specialities' can come the handiest, when it's their time to guide, help, teach you or give you something that can be helpful for your present and future, or help you understand the past; which is equally handy on the long run.
Lucifer has a lot to offer, but I'd say, first and foremost, enlightenment. Not just knowledge, but something beyond that. He pay close attention to those he cares about, and in fact, sometimes, the demons who reach out to you, can do thanks to his will. That's how far he is capable of 'caring', making sure you get the most fitting being on your side based on the stage of your life, the circumstances or simply allowing them to approach you, because yes, Lucifer has a saying in which demon is allowed to contact who.
Infernals also tend to reach out to those they had connection before, like from previous lives, or far beyond that material existence. They are sentinent beings, seeing more than our currently limited, human mind can, so if they show up, even if you may think that right now, it's not the time, it can still be a sign for later, which will encourage you the contact with that particular Infernal.
Genuine gratitude is something he'll feel right away. Cherish his intent, think about him, read about him, hear others speak about him, keep your eyes, mind and senses open, give him small offerings from your day if you feel like it, it doesn't need to be grandiose, at all. Pure genuinity comes from the most simple things rather than the 'flashiest'. Share your food, drink with him, offer him arts, dedicate candles, incenses to him, offer him place in your space, let his presence fill you.
