Most importantly of all, dragons lack either the consistent thermal output or the radar return of an aircraft, which are the main ways an F-15 locks onto targets. As a ground attack aircraft, the A-10 has a better chance of locking on to a dragon, simply because they are closer to the sorts of things an A-10 would be sent out to attack; bunkers and hardened positions that require video or laser targeting to lock on to.
If we're conceptualizing that the A-10 gets laser support, then why are we wondering if the F-15 can lock onto something in the first place?
Meanwhile if both are relying on their own internal ability to generate a firing solution, the issue the A-10 has is that it had trouble in tests using the gun to hit stationary tank targets on the ground (indeed it has a habit of creating blue-on-blue situations because of the difficulty of seeing things and the wide spread of the main gun) and the non-gun munitions are mostly ground-attack only (and are how the A-10 did most of its work in actual engagements anyway).
I think the issue of lock depends on the dragon. I wouldn't be willing to assume a large Metallic Dragon with golden scales didn't have an enhanced radar return, after all, and even large birds (vultures) have radar cross sections, just not very big ones (bigger than any modern stealth aircraft, though); trees similarly have radar cross sections which is why they're filtered out by modern radar based on their null velocity relative to the ground. Dragons are a lot bigger than vultures and could be expected to have a much larger radar cross section as a result, regardless of their scales, unless you assume their scales
happen to be made of radar absorbing material (when the "metallic" factor would if anything argue in the other direction).
Similarly, an ice dragon (like a White) might not have a strong thermal signature, but a fire dragon (a Red, Gold or Brass) is more likely to have something that's at least noticeable.
Based on this analysis I think the easiest dragon to target/shoot down would be a gold or brass dragon (metallic scales, Fire subtype so larger heat signature), and the hardest would be a Black dragon (not metallic, no abnormal heat signature, hard to see at night) or in daylight a non-Red Chromatic.
I have to say, though, I'm not volunteering to try it out. Or be nearby, really.