Use your natural network first. Ask your friends to make intros for you. Once you have a decent conversation with those people they can recommend you to other people they have worked with in the past.

People will treat outreach on linkedin as spam, because it is. They don't know you and you want info out of them, with little in it for them.

The ability to find and reach your ideal customer is paramount, and you're having trouble doing that. You've tried LinkedIn so far, but it's worth your while to experiment with other distribution channels.

You're trying to book meetings by reaching out ("cold") on LinkedIn in order to do what exactly? To have a conversation in which you could ask questions, and validate or invalidate hypotheses. One way to do that is to go public with your hypotheses in appropriate fora. The internet abhors someone being wrong, and your target customers will come out of the shadows and write essays proving just how little you know on the topic, and how wrong you are.

There's an old Algerian saying: "يرمي الراشي باش يجيب الصحيح", or "Throwing the brittle to pick up the solid" (meaning people who say something wrong (brittle) in order to get the correct (solid) information).

There's also "Cunningham's Law": "The best way to get the right answer on the Internet is not to ask a question; it's to post the wrong answer."

Or this: https://xkcd.com/386/

Now, you're not doing that out of deception of course. The very reason you're trying to develop a product for your target customers is that you believe some things to be broken and believe certain things to be true. You can write about those and get to validate or invalidate these beliefs. In any way, you'll get feedback and strike up conversations.

That is but one way.

>I have offered Lunch and coffee as an incentive.

That would be a courtesy, not an incentive. An incentive would be to pay them consulting fees and get them as consultants to answer your questions.

There are other ways: trade shows, conventions, subreddits, Quora, etc. Where do these people gather?

You also could think of changing your messages and state the questions in your email. This might lower the activation energy: someone might not want to meet you for coffee/lunch with an open agenda, but if you state your questions clearly in your email they might think "What the heck, I can write a reply in 10 minutes and get done with it. Good action of the day: check".

The bottom line is to respect their time, and one way to show that respect is to have your thoughts and questions in order. This helps get responses.

They might not be interested, but if they know someone who might be, they might refer you to that person.

If you have a way to be useful for the person, don't hesitate. There are so many opportunities to be useful for people by connecting them to your network and solving problems for them. Someone sells something, you know someone interested? Offer to connect the two. Hook people up.

Do a Show HN here with your product, however rudimentary it may be. Also, make yourself reachable (put your contact information and your product in your profile) so people can reach out to you even after it's no longer possible to reply to this thread. Keep channels open.