Is it forbidden for me to take out a loan to buy a house, knowing that I have sufficient funds but they are invested, and I did not inform my lender of that?

The default ruling is that there is no harm for a wealthy person to borrow money for their needs. Thus, there is no sin upon you for borrowing while you possess wealth. However, informing your relatives that you do not have sufficient money to buy the house is blameworthy lying, due to the Almighty's saying: "{Indeed, Allah does not guide one who is a transgressor and a liar}," and the Prophet's (peace be upon him) saying: "Beware of lying, for lying leads to immorality, and immorality leads to the Hellfire. A man continues to lie and strives to lie until he is written with Allah as a persistent liar." It is also one of the characteristics of the hypocrites. Therefore, you must repent from this sin and resolve not to return to it.