While I share Shed's general view about the cost of the LHR R3 project being excessive, let's not pretend that HAL is just building a runway.
The new runway is only 1% of the total scheme costs, or £182million according to
https://www.gov.uk/government/upload...est-runway.pdf
As for LGA, my understanding is that the scheme doesn't add any capacity at all. It just makes the place a bit nicer for passengers, as well as improving the taxiway layout so as to reduce delays. Whereas the LHR R3 scheme adds capacity of 50 million annual passengers, albeit rather expensively...