When you are ready to go into complicated business processes, the first step is branching; in other words, choosing both (or all) flows simultaneously instead of only one.

an AND-split

Choosing all means you want all applicable tasks performed simultaneously under clearly defined roles. In BPMN this is simply illustrated with multiple arrows.
For example, in the figure below, A: Hotel Reservation and B: Purchase Travel Ticket are simultaneously executed.

By the way, business processes are often called workflows, but it's actually very difficult to define a flow by imagining actually flowing objects.
This is especially true when drawing complicated business processes. We suggest imagining a train and tracks, instead of the typical water and river, or car and roads.
Trains can detach cars and proceed on different tracks, and they can come back together and proceed again as one long train.

In reality, though, branching the flow into two ways increases possible errors, such as if there is trouble on one of the tracks (Figure 3: There are no available hotel rooms), or if there is a problem with the trains reconnecting (Figure 3: Sum of hotel fee and ticket fee exceed budget).
Whenever possible, you should avoid enabling all (AND-split) or multiple (OR-split) choices, and stick to simple single (XOR split) choices.

Naturally, managing business processes (BPM) is only meaningful if you improve them.
For example, let's take the press release of Figure 2: if the initial drafts are of good quality, and also frequent enough, there's no problem.
But, in other words, this means it is entirely dependant on the staff in charge.

Do I have to?

Let's rewrite it so that the leader leads the process.

By the way, swimlanes are usually labeled with departments, and someone in the appointed department executes the task,
but it's also okay to label them with a specific person or position.