Not normally. A race effort for 4 miles should be higher than your LT. Even all the way up to a 10k would normally be higher. Plus HR levels under racing conditions are generally higher than training ones.
I'd suggest just going out and following the protocol for doing the field test and seeing what comes up. I'd also re-do your cycling one to compare to what you found before.
I heard that the middle 30 minutes of a 10k are acceptable alternative to a field test. BUT, I just chose to do the field test anyway as I didn't have a recent 10k race that I could draw from.