Signing LeBron means you are likely trading Hayward and in essence forcing out Irving. Without those 2, the C's were one game 7 away from the Finals. Adding them, to me, makes them a shoe in for a top 3 team in the NBA and barring anything unforseen, the best team in the East by a large margin.
Cs can stay pat and be contenders next year. Try to re-sign Smart/Baynes. Maybe add an experienced veteran for end of bench guy/mentor for young guys. This team will be contending next year. The championship window is now open.
If LeBron wants to sign for the the MLE, have at it. So basically not happening.
From a pure basketball perspective though, Boston is probably the best situation for LeBron. Stable owners, great GM/coach, roster with great depth and 2 all stars plus 2 possible all stars.