The Fanny Kaplan attempt at Lenin is an interesting one because she did, of course, actually shoot him — and, arguably, succeeded, though not as she would have liked, because, while it took several years, Lenin did in the end die as a result of his wounds from the assassination ‘attempt’.
Obviously, if Lenin had died immediately, it would have had immense consequences for the history of the Soviet Union; but, conversely, if her shots had missed entirely, or she had, for some reason or another, aborted the attempt, Lenin could have lived much longer, which also would have had immense consequences for both the history of the Soviet Union.
For example, in either case, Stalin’s path to power is much less clear; IOTL, Stalin‘s measures to take control of the Communist Party were very much facilitated by Lenin’s long decline. If he had died right off, Stalin was not in any real position to take control of the country and the party in 1918, and, if whoever takes over in 1918 (assuming the Bolshevik dictatorship doesn’t collapse entirely) gets themselves securely in power, Stalin isn’t going to have that same opportunity as he did in the 1920s. On the other hand, if Lenin survives relatively healthy and well into the 1920s, he probably has the chance to marginalize Stalin that it’s likely (though by no means not certain; accounts of “What Lenin Would Have Wanted” are a combination of conjecture, wishful thinking and propaganda come up with by the various sides after the fact with relatively in the way of reliable sources) that he had intended to do, which would, again, make Stalin’s path to power less clear.
Lenin’s long-term survival or his immediate death either causing the Bolsheviks to split early, or split later, or not split at all, or split but with Lenin explicitly leading one faction rather than the factions fighting over replacing him, has a whole host of consequences and butterflies to affect the rest of twentieth century history across the planet.