Itoje sustained medial ligament damage during England's 32-20 win over holders Ireland in their opening game and Jones said the 24-year-old Saracens player had made good progress with his rehabilitation.
"(Itoje) is coming along well," Jones told British media. "I might have to give him the hurry-up, because we've lost Courtney. We've lost three of our best forwards and we've got to be able to cope."
Apart from Lawes, prop Mako Vunipola (ankle) and hooker Dylan Hartley (knee) have also been ruled out for the rest of the championship.
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England host Italy at Twickenham on March 9 before playing Scotland on March 16 in their final game of the tournament.
(Reporting by Hardik Vyas in Bengaluru)
