Lord Taverne will ask the Government at question time "whether they plan to review the constitutional role of the monarchy". It's an interesing question on a number of levels. While in practical terms the monarch has very limited powers (Conventions govern the use of her powers - Bills which have been passed by both Houses of Parliament must be signed by the Monarch to become law, but by a 300 year old convention the Monarch doesn't refuse; the Queen "chooses" her Prime Minister - but her choice is limited by convention) - the Monarchy is central to the system.Parliament is called by the Monarch - and each session she tells members of both Houses in the 'Queen's Speech' what she would like them to consider (the speech is written by the Government); She dissolves Parliament (on the advice of the Prime Minister). It is "Her Majesty's Government" (often called HMG); We refer to the Queen's courts and judges.
The question could touch on the so-called 'Royal Prerogative' - defined by Dicey as "... the remaining portion of the Crown's original authority, and it is therefore ... the name for the residue of discretionary power left at any moment in the hands of the Crown, whether such power be in fact exercised by the King himself or by his Ministers". Key parts of the Prerogative are the subject of proposals for reform. (for further details see http://www.official-documents.gov.uk/document/cm71/7170/7170.pdf and the follow up documents on http://governance.justice.gov.uk/).
There aren't many Republicans in the House of Lords - but it might provoke some interesting exchanges.
