A possible solution: RNG (Random Number Generator)
To do this successfully and easily in Limesurvey it would need to be something like this:
A new question type that is called RNG (random number generator).
The person creating the survey would be able to define the scale of the RNG, for example they would input '3' when setting up the question. And therefore the RNG would be between 1-3.

Every time the user encounters this question on the survey it would be a behind the scenes process that randomly generated a number instead of getting user input. The user would not be aware it happened nor see the number they were assigned.

Now the admin of the survey can set future question conditions on the RNG for this user.
For example all users who were assigned:
1 - will see a kitten
2 - a puppy
3 - a wolf eating a dead animal
followed by a question.

To measure the effects of the images on the user response it has to be randomized when the user takes the survey.

Adding in a RNG question type, to silently assign the user a number, allows the admin to easily define the scale of the RNG and also add multiple instances of it throughout the survey.