What investments offer the most lucrative returns?

As well as safest

index mutual funds offer diversification (less risk) and steadily beat managed mutual funds over time (more lucrative returns). They also have a low expense ratio, menaning they are inexpensive to maintain, and that can save you a lot of money over time.

Vanguard and Fidelity (as well as others) have some excellent, low cost index funds available.

The two are not compatible. Greater return = greater risk.

Investing in stock mutual funds is a great way to give yourself exposure to higher returns and at the same time reduce risk. I said reduce not eliminate. Investments with high returns always entail risk but holding onto quality mutual funds for the long term is a great way to accomplish what you are seeking in your question. Please read my profile

It depends on how much risk you can take. The Chinese gov't has over a trillion dollars. They don't invest in companies or high risk debt, even though they could definitly accept the risk of that investment, they invest in very secure US gov't debt. It pays them 4% to 6% per year. The reason is that they want "guaranteed" returns.

If you want the biggest returns, the only guaranteed way to get it is to invest a huge amount of money. All other recommendations have potential to lose money.

The riskiest ones offer the greatest potential for return, but that might not be a good strategy.