Looking at the Vatican's website it seems Laudato si' is the first encyclical that has no official Latin version, while the previous one, Lumen Fidei, had. Is this true?
There is now an official Latin version. Encyclicals are always published in the Holy See’s official journal, Acta Apostolicae Sedis. Laudato si’ can be found in volume 107, no. 9, published in 2015.
For various pastoral reasons, primarily (as it appears) in order to reach a wider audience, Pope Francis wrote Laudato Si' in Italian (whence it was translated into Arabic, German, English, Spanish, French, Polish, and Portuguese). There may be a Latin version planned, but I can find no details of it.
This is not the first encyclical, however, which was not written and first published in Latin. The most notable recent encyclical written in a language other than Latin was Mit Brennender Sorge ("With burning sorrow"), addressed by Pope Pius XI to the bishops of Germany in 1937. The purpose of Mit Brennender Sorge was to condemn the actions of the German government, and it came with instructions to be read out to all parish congregations on Passion Sunday, 1937. This would explain why it was written in, rather than translated into, German.
Non Abbiamo Bisogno, also written by Pius XI, is another encyclical not written in Latin. This original was in Italian, and addressed to the bishops of Italy, denouncing certain actions taken by the government of Benito Mussolini against the Catholic Church.
And Pius XI was not the only Pope to write an encyclical in a non-Latin language: Pius X and Leo XIII both wrote such encyclicals—Pius in Italian, to the bishops of Italy in particular, and Leo in French to the French bishops.
Complicating the issue, there are some encyclicals listed on the Vatican website with Latin titles, and presumably therefore written in or translated into Latin, but lacking an available Latin text on the website.
Thus it appears that typically encyclicals are written in Latin, but not always; and when they are not written in Latin, this is usually because they are addressed to the bishops of one nation in particular.
It is quite possible that Laudato Si' is the first encyclical addressed to the universal Church (indeed, as the encyclical states in paragraph 62, "addressed to all people of good will") not to be written in Latin; that would take a comprehensive review of all encyclicals ever written. The texts available on the Vatican's website extend only back to the beginning of the papacy of Pope Leo XIII, in 1878. The website PapalEncyclicals.net contains a number of encyclicals and other papal writings of various types, listing many popes before Leo XIII. In that list, I see no other encyclicals per se that appear not to be written in Latin, yet are addressed to bishops of multiple nations. However, although I regard this website to be highly useful and very interesting, I have no assurance that it is complete; and some of the Latin titles may be of documents that were originally written in (for example) Italian, and later translated into an official Latin version.