A lazy GM still prepares a list of potential scenes, and thinks about the links that can lead from one scene to another. You don't necessarily need to have specific clues in mind so much as an idea that one scene will logically flow from another.
For example, say an assassin prepared poison from plants cultivated at the royal gardens, but mistakenly left a single leaf at the scene of the crime. All characters can find the leaf after searching, but the link to the garden comes via different channels. Character A with herb lore can identify it, and recalls that exotic flora is kept in the gardens. Character B with contacts in the city guard knows a watchman who patrols the gardens. Character C is a magic user who would know that wizards purchase rare plant components from the apothecary in the garden. Note that in the latter two cases, the party doesn't need to know anything about the leaf itself - it is the link to the garden that is important. However, Character A does have a chance to show off with a spend of herb lore, if the player wants to look cool.
Dynamic players won't wait for a list of clues, and might create links where you hadn't. For example, a ranger might think to look for footsteps, and you say there is some unusual-colored mud smeared at the crime scene which only comes from the garden. The player feels cool because he thought of the clue, and you feel clue because he did your work for you!
I will note in conclusion that being a lazy DM sometimes requires the ability to think on the fly in lieu of preparation.