Please refer to this diagram:

Let's look at some typical workflows:

1. take a walk-in rental.  Use the LS -> BRM workflow
2. take an advanced rental.  As above, but just 'return' from BRM, only take the payment when the customer actually pays
3. take an online rental.  Secure the booking by getting them to leave credit card details in stripe when they book.  This makes it likely they show up.  Then, when they show up & pay you get them to pay via lightspeed*

• even if you have card details stored in Stripe you can't 'get that data out' of Stripe.  You can charge the card via Stripe, but you can't extract the card data to process elsewhere.
  
• N.B. you may want them to pay 50% or even 100% when they book online.  You can do this, but please beware that these payments will flow through your Stripe account, and cannot flow through lightspeed, which is why we recommend if you're using Stripe you configure your OBW to take card details only when the book online, and full payment in-store using lightspeed.  See option 1 here
  
• you only need to process payments through stripe under exceptional circumstances - like a no-show.  Or they break a bike during rental and refuse to pay.  All regular payments for rentals, extension, even damage would normally be taken in-store using lightspeed.  So Stripe is acting like a free insurance policy for these exceptional circumstances.

• one payment platform to reconcile payments (lightspeed)
• one place to see all your transaction reporting (lightspeed)
• (and it doesn't stop you securing online bookings with the help of stripe - by taking card details)