Have you tried rebooting your phone?
I've been seeing this as a suggested solution to most issues. Is iOS starting to become like Windows?
I tried testing to see if my phone has the same LTE delay issue.
Scenario 1:
Lock phone
Double-tab home button, close Safari
Lock phone
Unlock phone
Open Safari > go to macrumors.com
Result: Page loads within 2 seconds
Ask Siri a question, she responds instantly
Scenario 2:
Lock phone
Unlock phone
Open Safari > go to apple.com
Result: Page loads within 3 seconds
Go back to home screen
Open Safari > go to cnn.com
Result: Page loads within 3 seconds
Lock phone
Unlock phone
Open Safari, close all tabs, open new tab > go to yahoo.com
Result: Page loads within 4 seconds
Lock phone
Unlock phone
Ask Siri about yesterday's baseball scores, she responds within 2 seconds.
I don't think my phone has this issue. This is at my home with 2-3 bars. At my office in San Francisco, I get 4-5 bars, but LTE is way slower (probably because there are so many users in the city). Sometimes pages take 5-10 seconds to load web pages.