He said Mrs May must remember she is the PM of all parts of the UK.
Lord Alderdice was speaking in the House of Lords as peers considered the government's Brexit bill.
He was speaking in support of an amendment that insists that no hard border is put in place between NI and the Republic of Ireland after Brexit.
The amendment proposed by former Northern Ireland Secretary Lord Hain stated that an open border must continue in line with the provisions of the 1998 Belfast Agreement.
After hearing government assurances during the debate, Lord Hain later withdrew his amendment.
Lord Hain, who was Northern Ireland secretary of state from 2005 until 2007, said: "If we get this wrong, for the UK, it may be perilous. For Northern Ireland it could be politically lethal."
Lord Alderdice, a Liberal Democrat peer who voted Remain in last year's referendum, said that Mrs May must not view the issue of the border as if she was still home secretary.
He added that it was his fear that the government was looking at this with "the approach of the Home Office".
He also called on Mrs May to approach the issue of the border with "imagination" and "political creativity".
In response, Lord Trimble, the former Ulster Unionist Party (UUP) leader who sits on the Conservative benches, rejected the amendment supported by Lord Alderdice and Lord Hain.
Lord Trimble told peers he did not believe the amendment was necessary.
He said: "The amendment is asking the Prime Minster to support the maintenance of the open border between Northern Ireland and the Republic of Ireland.
"The Prime Minister does that as of now. It is in the White Paper. It is not necessary."
Former Conservative minister, Lord Howell, supported Lord Trimble's position on the amendment.
Former UUP leader, Lord Empey, said the amendment was "misplaced".
He told his fellow peers that he agreed totally with "an open free border".
However, he called on the government to give an assurance that "there will be no internal border in the UK".
Baroness O'Loan told a packed chamber that she opposed the amendment.
She said it would not "benefit the UK" and that the issue of the border should be "dealt with in the negotiations".
Lord Kilclooney, the former Ulster Unionist MP, also opposed the amendment and told the house that the "southern Irish were petrified about Brexit".
Earlier, Lord Hain said Brexit could cause "profound damage" to the peace process and warned that a return to checkpoints along the border would sew division and discontent.
Responding for the government, Lord Dunlop said there was no need for Lord Hain's amendment.
He said the "government's intentions are clear" and that no undertaking was "necessary".
The peer, who represents the Northern Ireland Office, added that maintaining the Common Travel Area with the Republic of Ireland "will be a priority".
He said the government is seeking "practical solutions" to achieve as "frictionless a border as possible".
At the end of the debate, Lord Hain withdrew his amendment.
His move came as peers began the detailed committee stage debate on the European Union Notification of Withdrawal Bill.
The legislation has already cleared the Commons without amendment.
The former Alliance leader Lord Alderdice has said Theresa May must not view herself as being "Prime Minister of England and a few add on bits".