For further information, the key amendments are numbers 19, 20, 37 and 39 (the numbers are as set out in “Bill 212 2017-19, Lords Amendments to the Bill, 17 May 2018).
19 is a new clause: “Parliamentary approval of the outcome of negotiations with the European Union.” It requires approval of the withdrawal agreement by Act of Parliament, and prevents exit without an agreement without Parliamentary approval. It is the most important of the amendments.
20 requires “approval by Parliament of a mandate for negotiations about the United Kingdom’s future relationship with the EU” before a Minister can issue regulations to implement the Withdrawal Agreement. This is important because the outcome of the negotiations that Parliament agrees as a result of amendment 19 may leave the future relationship vague.
37 and 39 reverse the amendment made in the Commons fixing Exit Day. It means that a Minister has to set the Day by regulation. This is important because, the way the Bill is drafted, it is needed to give force to amendment 20, and to the requirement that Parliament approve “the final terms of withdrawal” by statute (‘Amendment 7’ introduced by Dominic Grieve on which the Government was defeated in December).