Technically the Celtics could renounce Allen and Pierce (if he ops out) and sign James.
How so? The cap is estimated to be somewhere between $50 and $53 million next season; let's take the high number.
1. KG - $18,832,044
2. Rondo - $9,100,000 (approximately)
3. Rasheed - $6,322,320
4. Perkins - $4,890,208
5. BBD - $3,000,004
6. roster charge - $457,588
7. roster charge - $457,588
8. roster charge - $457,588
9. roster charge - $457,588
10. roster charge - $457,588
11. roster charge - $457,588
12. roster charge - $457,588
Renounced: Paul Pierce, Ray Allen, Eddie House, Marquis Daniels, Shelden Williams, Brian Scalabrine, Tony Allen, Bill Walker, J.R. Giddens, Lester Hudson
Total: $45,347,692
$53 million - $45.35 million = $7.65 million
Lebron isn't going to sign for less than $8 million in his first year, when he's eligible for around $16 million+.