Additionally, there was an issue regarding the Translantic Trade (Alliance?) or Partnership, which citied this very situation where corporations could potentially sue the government if they did not get to deliver services, such as NHS and local government
You are referring to the Transatlantic Trade and Investment Partnership (TTIP), a proposed trade agreement between the EU and the US. If we leave the EU it will not apply to the UK. Negotiations between the EU and the US have been ongoing for 6 years and look set to continue for several more years.
Opponents of TTIP claim that it will force privatisation of the NHS or make privatisation impossible to reverse. The EU says that the agreement will preserve the government's freedom to run the NHS and other public services. If the EU is right this will stop the NHS being forcibly opened up to US companies. Since the final text has not yet been negotiated, there is no way of checking. The EU may be hiding something or there may be a loophole in the final agreement that US companies will be able to exploit. But, if the EU is right, there is no threat to the NHS.
The government has said the NHS is not on the table in trade talks with the US (or anyone else). Trump u-turned the day after saying that the NHS was on the table. He said, "I don’t see it being on the table. Somebody asked me a question today and I say everything is up for negotiation, because everything is. But I don’t see that as being, that's something that I would not consider part of trade. That’s not trade." Until a deal is negotiated we have no way of knowing.