TL;DR
In the context of "INVEST," independent doesn't mean there are no prerequisites or dependent activities. Rather, it means that a given unit of work can be estimated, performed, and tested as a unit within a single iterative cycle (e.g. one Sprint).
It often helps to break up time-spanning items into smaller activities that can function as prerequisites, while still being performed separately from dependent backlog items. This will allow Product Backlog items to meet INVEST criteria even when the dependent features (think epics or themes) might take several Sprints to complete.
Decompose Work Into "Sow" and "Reap" Activities
Some tasks involve a small amount of time from a team member, let's say 1 story point, but the definition of done for that story involves ordering parts that have a certain lead time that might span one or two sprints.
The best way that I've found to handle low-effort but time-spanning tasks is to decompose them into discrete actions. In farming, "planting" and "harvesting" are part of a long-term cycle, but can be represented as separate activities.
Using your own example of ordering parts, there's an external dependency on the ordering process and the vendor. You might split the story into multiple low-effort items that don't all have to performed within the same time box.
Place order for widgets needed for a future story.
As a team member,
we need to order a box of widgets
so that we can integrate a widget into our thingamajig.
Follow up on widget order if not received before starting the dependent user story.
As a team member,
we need to get tracking information on our widget order
so we'll know when our widget-integration story is ready for Sprint Planning.
Unpack & verify widget.
As a team member,
we need to get the box of widgets from the mail room &
verify the contents
so that we'll know we have the widgets on hand for integration.
Plug widget in.
As a widgetologist,
I want a widget integrated into my thingamajig
so I can frobnosticate the embiggener.
As a practical matter, you might order the widget in the current Sprint. During Backlog Refinement or Sprint Planning, the Scrum Team would then pull in the appropriate follow-up stories as needed. During planning events, the team would also consider whether all of the prerequisites needed for the widget-integration story (such as having the needed widgets on hand) have been satisfied.
Some of the follow-on stories are obviously be dependent on having already ordered the widgets, or already having received the ordered widgets. Nevertheless, getting tracking information or unpacking/verification would be prerequisites to stories that assume the presence of the widget, and these stories could be pulled into a Sprint or removed from the backlogs as necessary. For example, since unpacking and verification of the order can be performed independently of using a widget, the story meets INVEST criteria.
This general pattern of treating an initiating activity and a closing activity is widely applicable to a variety of time-spanning dependencies. It seems to address your given use case, and the pattern is widely applicable to many types of stories that would otherwise violate core principles by spanning multiple Sprints.