Under the scheme, resident individuals can acquire and hold immovable property or shares (listed or otherwise) or debt instruments or any other assets outside India, without prior approval of the Reserve Bank. The word otherwise can be interpreted as any other non-listed , new company etc,
Further , the RBI circular notifies the investment in shares as
Indian investment abroad in equity capital (shares)
It does not specifically state not in the shares of new companies in abroad
Hence , according to me , there is no bar in investing in new company shares in abroad under LRS Scheme up to $ 75000 per FY.