Lenders don't specifically base their CLI decisions on CLI's granted to you by other lenders, but rather on review of your soft-pull (usually) credit report and their own credit scoring models, as well as your history as a customer of theirs. That being said, they do look at how much revolving credit you have (and how much of it you use, which is why utilization control is important) as part of their monthly review of your credit profile, so seeing boosts in your credit limits could be one factor to positively influence their willingness to give you CLI's (unless they've got a hard limit of some kind, for instance, on how much revolving credit you can be extended). Again, though, a combination of your history with the lender and your overall credit health is most important. I'm fairly sure, for example (though this is for a new account, rather than specifically CLI) that having open accounts with Synchrony in good standing over the past 18 months, plus my overall credit history, were factors in getting my new PayPal MC several weeks ago.
