I think there are a couple misunderstandings here, firstly about the nature of Republican (and imperial) politics and secondly about the nature of the lictors. As far as I can tell these two misunderstandings are setting up an unrealistic foundation to the question, which if rephrased is not a bad one: how was the loyalty of those close to important people at Rome ensured, and did political opponents of these people ever encourage or utilize the disloyalty of those close to them to have them assassinated?

Despite what HBO would have us believe, the Republic was not a period of blood-soaked assassination and backstabbing. There are vanishingly few assassinations or assassination attempts during the Republic. There's Caesar, the curious case of the tribune Livius Drusus in 91, the very curious (and extremely poorly attested) case of the praetor Sempronius Asellio in 89...that's basically it. I don't know, maybe there's one or two more that I'm forgetting about. P. Clodius threatened Pompey with assassination in 58 by sending a slave into a meeting of the senate carrying dagger, which he dropped in front of Pompey. How serious this purported attempt was is anybody's guess. More commonly, people were killed during outbreaks of civil violence or as the result of sedition. Hence Clodius' death (which Asconius says was murder, but not premeditated), the deaths of both Gracchi, presumably the deaths of Memmius and Ninnius (?) that Plutarch and Appian say were killed by armed mobs on the orders of Saturninus and Glaucia, possibly the deaths of Saturninus and Glaucia themselves (stoned to death by a mob according to Appian, but executed publicly in the forum by Marius after surrendering themselves during their sedition according to Plutarch). A couple more spurious instances could probably be added to the list, without much to be gained. Scipio Aemilianus, for example, was rumored by the Romans to have been murdered on the orders of C. Gracchus' friends--Plutarch suggests Gracchus' ally Fulvius Flaccus, Appian offers Gracchus' mother (and Scipio's mother-in-law) Cornelia--but the rumors were never substantiated, nor was the cause of death ever agreed upon (the Epitome of Livy has his wife poisoning him, while Velleius has him strangled by the neck, whereas Appian preserves a rumor that he actually committed suicide). Scipio died relatively young (Velleius says he was 56), but he wasn't that young, and the evidence isn't strong enough to support murder as the only cause of death. The point is that most political killing in the Republic can't really be called assassination, but was the result of much larger episodes of violence and disorder. We could go into the nuance of what constitutes assassination, and how that lines up with Roman concepts of vis and related crimes, but targeted private or, as in the case of Caesar and Livius Drusus, at least individual political killings are not in fact common in the Republic in the first place.

Moreover, a purely statistical analysis of imperial assassinations is highly misleading. If you look at Wikipedia's list, only two emperors on there predate the end of the second century, and the resulting disorder that followed the extinction first of the Antonines and then a few decades later the Severans: Caligula and Galba. Galba is a bad example. He ascended to the emperorship in a time of civil war, the Year of Four Emperors (69), when as Tacitus points out several imperial claimants popped up, with different bases of support. The complex relationships between different groups during those months is beyond our scope, but Galba had been made emperor with the support of the army and especially the Praetorians, and quickly made a number of decisions that made him very unpopular with the very same people who had put him in power. As a result, he was removed by a conspiracy. But it's worth noting that Galba wasn't killed by a small group of conspirators who ambushed him a la Caesar. Rather, Galba was killed essentially in a mass mutiny of his troops, in the streets (Suetonius says that he went out into the forum). This is in sharp contrast with Caligula, who was killed by a conspiracy of only a few men, who ambushed him without warning. Suetonius draws obvious and explicit parallels with Caesar, reusing much of the imagery of his account of Caesar's assassination and even claiming that some of the conspirators stabbed Caligula in the groin, which is where Plutarch claims that Brutus struck Caesar.

Of the other examples on the list (the comprehensiveness of which I'm not actually sure of), they were all killed either during the Third Century Crisis or during the confused and chaotic period of civil war following Commodus' death. Commodus, moreover, also requires some nuance, because I don't think his assassination "by" the Praetorians is the kind of thing that you're actually talking about. Commodus wasn't killed at the hand of a Praetorian, he was killed as a result of a conspiracy. Dio--or rather, Dio's epitomator--says that Commodus was killed as part of a conspiracy of three people: his mistress Marcia, his cubicularius (kind of like a chamberlain) Eclectus, and the Praetorian Prefect Aemilius Laetus. Dio's epitome gives little indication that the Praetorians in general were involved. The epitomator says that they poisoned him, and when he vomited up the poison they had an athlete named Narcissus strangle him. Herodian disagrees in some of the details, but agrees with the story in general.

If you figure that that counts as being assassinated "by" the Praetorian Guard, then great. But the more important point is that by this period the Praetorian Guard was not a bunch of imperial bodyguards. They were not, really, bodyguards at all. Already by the time of Galba's death the Praetorians had ceased to be the close bodyguards of the emperor. Suetonius says that when the army mutinied against Galba, a unit of German troops tried to come to his aid. Similarly, Suetonius also says that when the conspirators fell on Caligula they were dispersed by the emperor's German bodyguard, who killed some of them in the fighting. From a very early date, the personal guards of the emperor were not the several-thousand strong Praetorians, but a much smaller group of men, the composition of which don't really matter and which changed over time. It's a little hard to describe the Praetorians in modern terms--they were part riot police, part Guards unit (as distinct from personal bodyguards), part executive body/sometime bureaucracy headed by the Praetorian Prefect--but they were a very large group, with predominantly political and class purpose. During the Third Century Crisis, when most of these assassinated emperors were killed--indeed, when the overwhelming majority of imperial assassinations took place--the army, headed by the Praetorian Guard, was effectively in control of the imperial office. The third century was a period of internal fragmentation and civil war, resulting in massive decentralization and military crisis. In this context, the imperial office essentially represented the leadership of the army--hence the "barracks emperors" of the third century, who were chosen by the armies on the frontier, typically to respond to some kind of military crisis, and who were quickly removed once they outlived their usefulness. What you're looking at is not the closeness of the Praetorians to the emperor, but rather the near breakdown of imperial authority during the third century, during which period only a relatively few bodies of state remained centralized and powerful enough to maintain the influence necessary to keep things running--chief among these, the army, led by the Praetorians, its most politically-connected body.

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