Lend-Lease travelled through three main pathways. The first was the Arctic convoy route. This ran from Iceland to the Russian ports of Arkhangelsk and Murmansk - Arkhangelsk was only accessible in the summer, when there was little ice present. Ships from British or American ports would rendezvous off the Icelandic coast at Hvalfjörður, before steaming eastwards to Russia. They would return along the same route after they'd been emptied. This was a dangerous route - it was threatened not just by U-boats, but also by aircraft and surface raiders. Several naval battles were fought to protect the convoys, most notably the 1942 Battle of the Barents Sea and 1943 Battle of North Cape.

The second main route was the North Pacific route, running to Vladivostok. As you note, the Japanese controlled the sea routes that these ships would use. However, the Japanese government was not at war with the Soviet Union, and had no desire to start such a war, as to do so would open up a front that they were unlikely to win. This meant that Soviet-flagged ships had free access to the ports. As such, a number of American merchants were transferred to Soviet control. They were joined by older Soviet ships, which were unsuitable for the Arctic route due to a lack of speed. Once the supplies were offloaded in Vladivostok, they were shipped west along the Trans-Siberian railway. There was also an air route linking Alaska with airfields in Siberia, used by lend-lease aircraft. While the ships should have, in theory, been safe, there were occasional cases of mistaken identity, with ships on this route being sunk by both Japanese and American subs.

The final route was an overland route through Iran. In August-September 1941, both the British and Soviets invaded Iran (then Persia), due to concerns over pro-German sentiments in the Iranian government. The invasion also helped secure British oil supplies from the wells and refineries of the Anglo-Persian Oil Company, and the railway route to the Soviet Union. The British (and later the Americans) occupied the southern part of the country, while the Soviets occupied the north. Supplies were shipped to ports on the Persian Gulf, where they were transshipped onto the Trans-Iranian Railway, which ran northwards to the Soviet border.