The Russia of Look to the West both appears to be poised on the brink of greater expansion than OTL, yet at the same time has been plagued by a destructive civil war.
The key difference from OTL is that Peter III successfully survived an attempted coup by Empress Catherine (who in OTL became Catherine the Great) and had her and her supporters exiled to Yekaterinburg. The timeline assumes that the view of Peter III in OTL is mainly due to official Russian history being coloured by Catherine's prescriptions, and Peter III in Look to the West is a reasonably capable, if quixotic, ruler. Because he was not responsible for the withdrawal of Russia from the Seven Years' War like OTL, he is not as unpopular with the Russian people.
Peter III's Russia cultivated an alliance with the rump Royal Prussia that resulted in the War of the Polish Partition, buying off Sweden with Courland and defeating Austria. Lithuania was made independent from Poland and Peter III made his son and heir, Crown Prince Paul, its Grand Duke. Paul's policies proved enlightened enough that the Lithuanians became amenable to the arrangement. When Peter died and the Potemkin brothers, sons of Catherine, launched a coup, the Lithuanians supported Paul in his successful bid to win the throne back.
Peter and Paul's reigns have been much more peaceful than OTL with respect to Turkey, with Russo-Ottoman conflict being restricted to border skirmishes and vigorous diplomatic duelling. In some ways this has undermined their popularity with some sectors of Russian society.
Russia has also seen more expansion into the insular Far East, with trade missions aimed at Japan headed by Moritz Benyovsky (OTL's Moric Benovszky) and including Lithuanian participation. However, trade seems to be the last thing such missions will accomplish…
Under Paul, Russia was involved in the closing stages of the Jacobin Wars and the Congress of Copenhagen reflected this, with Navarre becoming an independent state under a Lithuanian king and Russian influence. In the Watchful Peace, Russia intervened in the Ottoman Time of Troubles, conquering territory in Moldavia and the Caucasus and annexing the Crimean Khanate. In the Popular Wars, the brief War of the Russian Succession occurred when Peter IV, considered too Lithuanian from his rule there and too radical, was assassinated. In the end he was succeeded by his brother Theodore rather than his son Constantine. This meant Lithuania became more separated from Russia in her foreign policy. Russia has also supported the Stockholm Conspiracy of Swedish nationalists and suffered from Zionist intrigue in Crimea.
1727-1730: Peter II
1730-1740: Anna I
1740-1741: Ivan VI
1741-1762: Elizabeth I
1762-1795: Peter III
1795-1799: Civil War - Paul I (Romanov claimant) ; Alexander I (Potemkinite claimant)
1799-1829: Paul I
1829-1831: Peter IV
1831-1832: War of the Russian Succession - Constantine I (Legitimist claimant) ; Theodore IV (Slavicist claimant)
1832-1872: Theodore IV
1872-1885: Paul II
1885-????: Peter V