If a minister outright lies to Parliament then members of Parliament can ask the Speaker to refer it to relevant committee's or table a motion. If Speaker agrees then Parliament can attempt to find the Minister in Contempt and the Minister would be expected to resign (or resign before the vote).

During a debate, the Speaker can expel a member if they continuously or grievously breach rules but will usually just try to keep debates moving (speaker can curtail a speech if need be), keep things from boiling over, ensure speeches are within a time limit, rules obeyed and select which backbenchers (beyond a set already chosen for PMQ's) get called to ask questions. It is up to MP's to try to get the best answer they can from a minister, the Speaker doesn't have quality control bar ensuring timely and on top topic, Speaker would be getting dragged into a major (and timely) controversy if deciding if each and every ministerial answer was sufficient.

The Speaker, as well as role in ensuring the Commons and the staff run properly, has various powers: decides on points of order and questions of precedent, can summon a minister for Urgent questions, can decide if parliament is recalled for an emergency, selects which amendments will get debated (such selections can be key), can block a government bill if feels is trying to jam through a bill that already failed. The predecessor (John Bercow) became a figure of controversy with one government (David Cameron in 2015) trying to force him out and during the Brexit debates Bercow's decisions on what was permissible, time tables and other matters became major issues due to impact they had on government Brexit bills.

You might try the Institute of Government's article on role of Speaker from back in 2019