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The cheapest & fastest way to invest in a business in Spain is by the IBEX stock exchange.

As per my knowledge, the non-lucrative visa does not let you work

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If you have a non-lucrative visa, you are not allowed to work and earn money.

As noted by others this visa type you hold is for those of "ïndependent means" and doesn't allow work. The specifics of the visa state:

This visa can be requested by third-country nationals who wish to reside in Spain without carrying out any work or professional activity.

However, I doubt this precludes you from investing in a business. It just precludes you from being employed by or otherwise drawing an income from the business. As this is usually the point of investing, this probably doesn't help you. :-) And, officially, working unpaid is still working.

You might be able to do some cloak-and-dagger stuff where the business pays dividends offshore, or employs a mystery overseas (UK maybe) contractor. But probably you'll have to just bite the bullet and get a different class of visa (such as investor visa).

Once you have a visa/residence, business plans are not a requirement for investing. It's your money, you can spend it how you want. However, to apply for an investor visa you may well have to provide one (probably with proof of a wodge of capital too).

As you're already legally in Spain, I'd suggest it might be worth chatting to an immigration lawyer who can advise on what you can plausibly get away with, or whether there's an easy change of status he can apply for.