After obtaining Portuguese nationality there will be no minimum stay requirements or obligation to live in the country. You can move to another Schengen country, and you should register as an EU citizen living in a different country (Certificate of Residence for EU citizens) according to the country's specific internal procedure.
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What are the requirements for a naturalized Portuguese citizen to live in another Schengen country?
I'm an American citizen in the intermediate stage of learning Portuguese in order to obtain Portuguese citizenship. If I want to move to a Schengen country (Italy, France, or Spain) am I required to spend a certain number of days in Portugal and maintain a long-term lease residence?
Answers
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Once you acquire Portuguese nationality, there is no minimum period of stay in Portugal or any other requirement. If you want to relocate to another country in the Schengen area, there is no problem. In that case, to live in that other country, you will have to do the CRUE, which is the registration of a citizen of a European Union state to live in another one of the EU states.
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Any Portuguese citizen can live in any other Schengen country just with the passport and without being subject to a minimum period of stay in Portugal or in the other Schengen country.
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After obtaining Portuguese citizenship, and as an EU citizen, you have the right to move to any EU country to live, work, study, look for a job or retire. You can stay in another EU country for up to 3 months without registering there but you may need to report your presence. The only requirement is to hold a valid national identity card or passport. If you want to stay longer than 3 months, you may need to register your residence. In many EU countries, you need to carry an identity card or passport with you at all times. In these countries, you could be fined or temporarily detained if you leave your identity documents at home - but you cannot be forced to return to your home country for this reason alone. There is no obligation to spend any number of days in Portugal or maintain long-term lease residence.