I think that was the original plan back in 2015. Then CAS -- ACM Sohail Aman -- wasn't enthusiastic about buying a LIFT and AHQ at the time felt that the JF-17B would be enough. They cited operational costs being a big issue. It's possible that the cost of flying the L-15B has gone down since then (it was just entering production 10 years ago). Or, potentially, they're now practically finding that the learning curve between the K-8 and JF-17B is still too high, hence the need for a LIFT to help bridge the middle.
I also think there may have been a change in strategy by the end of ACM Aman's tenure, i.e., to have GDPs to build a career around a specific platform rather than jump between them. Before, a GDP would start on the F-7P and then move onto the F-16 a few years later, for example. However, now, the PAF wants pilots to start training on the multirole fighters as early as possible and to stay on them for as long as possible; moving forward, you'll start and spend most of your career on one of the F-16, JF-17, or J-10. This way, you get people who develop lots of skill, experience, and familiarity with one platform, and you keep those gains instead of constantly resetting when you send someone to a new jet.
However, the F-16, JF-17, and J-10 aren't necessarily simple enough for someone coming off a K-8. They're all high-value assets that you both want to fully leverage (lots of tech in them), and to minimize accidents and mistakes. You still need 'experienced' aircrews, and as a result, something like the L-15B could provide that environment. Basically, once you're done on the L-15B, you get assigned to an F-16, JF-17, or J-10 unit.
BTW, there are some smaller logistics benefits of this approach too. For example, the JF-17B3 and J-10CE use a HMD/S that requires custom fitting; so, when the PAF invests in that kit for a pilot, it'd prefer that kit be used for as long as possible. You'd rather give that kit to a new pilot who'll use it for the next 7-10 years. However, if you're going to put someone new on the JF-17B3 or J-10CE, you'd want to make sure they're trained to use their fighter.