Note: Vast oversimplification follows

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Crimea 1854-1856: Tsarist forces move into Ottoman Turkish territory. British & French help Turks engage and quickly drive Russians back out of disputed territory. Probably should have quit right there, but tried to take Sevastopol. Russians lose a close one at Balaclava, get pushed back again at Inkerman. After a lot of sickness (cholera), inept supply and stupidity, Sevastopol falls to British/French/Turks and war is ended by the Treaty of Paris.
That about what you were looking for?
Vast oversimplification of The 1918 Russian Intervention follows

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Allied war supplies were stored both at Murmansk and Archangel. An Allied representative who saw the supplies wrote that there were "acres on acres of barbed wire, stands of small arms, cases of ammunition and pyramids of shells of all calibres; great parks of artillery, motor trucks, field kitchens, ambulances--thousands of them; railroad iron, wheels, axles, rails, coils of precious copper telegraph wire; most important of all, the regularly piled, interminable rows of metal pig--the alloys so essential for artillery production--and the sinister looking sheds where the T.N.T. was stored."
The Allies thought the Bolsheviks might be working with the Germans (Remember that Lenin was sent back to Russia on a German train), and so were afraid of the possibility that the supplies would fall into German hands.
Meanwhile, there was a lack of food in North Russia. Two British food ships were sent to Archangel trade food for the Allied war materials, but that was refused. Later the contents of one of the food ships was traded for the release of foreign nationals who were trying to leave Russia by ship from Archangel.
The British and the French were pressing the U.S. to send three U.S. battalions to North Russia. In a memorandum on July 17, 1918, President Wilson yielded to these requests "in the matter of establishing a small force at Murmansk, to guard the military stores at Kola, and to make it safe for Russian forces to come together in organized bodies in the north."
Wilson went on to say that these U.S. military units were not to take part in an organized intervention in the Murmansk or Archangel areas, and that he would withdraw them from Russia and send them to France if offensive use of the Americans troops came to pass.
President Wilson thought he was sending the 339th Infantry to guard supplies at Murmansk, but the British had a different Russian strategy.
To make a long story short, a small multinational force at the end of a very long supply line, operating for the dubious purpose of trying to influence the Russian Civil War... eventually withdrew.
The US troops got a new American commander who arrived at Archangel in April 1919 with orders to withdraw. As soon as navigation opened in June, the American forces left northern Russia.
British troops withdrew a few months later, but the anti-Bolshevik government they left behind held the city until February 1920.
American forces numbered about 5000; between Sept 1918 and May 1919 many minor operations
against the Bolshevist forces took place, resulting in more than 500 American casualties.
BTW, Allied forces also intervened in Siberia about the same time and with about the same result.
With the withdrawal of Russia from the war against Germany, the 40,000 strong Czech Legion, which had been fighting with the Russians against the Germans, began a slow retreat eastward, through the Ukraine, and then into Siberia. The allies had decided to remove the Czechs from the port of Vladivostok and transport them around the world to the western front in France, but on their way across Siberia on the Trans-Siberian railroad, conflicts developed between them and the Bolshevik officials along the route, which by May had become open warfare.
Another multinational force, including 70,000 Japanese, 829 British, 1,400 Italian, and 107 Ammahese troops under French command were in Siberia. Canada sent troops both on the task force to northern Russia and to Siberia.
About 8,5,00 men, primarily from the US 8th Infantry Division were deployed. There were several encounters with armed partisans that resulted in the death of 36 Americans.
So the "Russian Intervention" involved two diffent sets of US troops working with other multinational forces. All did relatively little fighting and casualties were relatively light. Nothing much was accomplished.
Do I get a passing grade in history now, Professor Storm?
...and no, I don't think Lend-Lease won the war.
Do you think Russia didn't need it at all?