The precise term for nationalization is expropriation and states have an inherent right to expropriate property owned by aliens. Claiming that it is a right is quite a strong claim, but it how it is. From chapter Expropriation in Principles of International Investment Law (2nd Edition):

Consistent with the notion of territorial sovereignty, the classical rules of international law have accepted the host state's right to expropriate alien property in principle. Indeed, state practice has considered this right to be so fundamental that even modern investment treaties (often entitled agreements "for the promotion and protection of foreign investment") respect this position. Treaty law typically addresses only the conditions and consequences of an expropriation, leaving the right to expropriate as such unaffected.

These strong words means that there is, in principle, a right to expropriation which is comparable to the right to self-defense.

The chapter continues with a discussion on what is required for an expropriation to be lawful:

It is today generally accepted that the legality of a measure of expropriation is conditioned on three (or four) requirements. These requirements are contained in most treaties. They are also seen to be part of customary international law. These requirements must be fulfilled cumulatively:

a )The measure must serve a public purpose. Given the broad meaning of ‘public purpose’, it is not surprising that this requirement has rarely been questioned by the foreign investor. However, tribunals did address the significance of the term and its limits in some cases.

b) The measure must not be arbitrary and discriminatory within the generally accepted meaning of the terms.

c) Some treaties explicitly require that the procedure of expropriation must follow principles of due process. Due process is an expression of the minimum standard under customary international law and of the requirement of fair and equitable treatment. Therefore, it is not clear whether such a clause, in the context of the rule on expropriation, adds an independent requirement for the legality of the expropriation.

d) The expropriatory measure must be accompanied by prompt, adequate, and effective compensation. Adequate compensation is generally understood today to be equivalent to the market value of the expropriated investment.

In your example, the asset was expropriated without compensation and would have been unlawful. Exactly how much a state should pay for expropriated property is a thorny subject. You can read more about it in Compensation for Expropriation Best Practices Series - March 2013 published by the International Institute for Sustainable Development and in Expropriation: a Sequel published by the UN body UNCTAD. The latter writes:

The last condition for an expropriation to be lawful is that it must be accompanied by compensation. Different methods of valuation may be employed to determine the amount of compensation (see sections I.F.4(iv) and III.B) and may lead to varying results. The differences between compensation for lawful expropriation and reparation for unlawful expropriation are discussed separately in section III.A.

In recent IIAs, there is an increasing level of convergence regarding the standard of compensation that must be paid to render the expropriation lawful. One of the salient trends among IIAs is that most of them incorporate the standard of prompt, adequate and effective compensation, also known as the Hull standard (see UNCTAD, 2007, p. 48).

Compensation is considered to be prompt if paid without delay; adequate, if it has a reasonable relationship with the market value of the investment concerned; and effective, if paid in convertible or freely useable currency. In spelling out what constitutes an adequate compensation, treaties most often refer to an investment’s fair market value.