All of those states have forms instructions that explain why those W-2s look that way, and how you handle the returns to minimize double taxation.

Full-year MA resident: The W-2 is correct. All wages are taxable to MA, Other State Tax Credit permitted on Line 30.

NY Nonresident: The W-2 is correct. Use Schedule A of Form IT-203-B and Screen 55.092 of Lacerte to determine how much is taxable to NY. 

RI Nonresident: The W-2 is correct. Use Part 2 of Schedule II in the RI-1040NR booklet. Lacerte unfortunately appears to only support Part 1 of Schedule II, and all of the related Help links (https://proconnect.intuit.com/community/help-articles/help/rhode-island-part-year-nonresident-freque...) are dead so I don't know if there's a suggested kludgy workaround. Sorry!