Visiting the Museum of London, Science Museum, Victoria and Albert Museum (briefly), Imperial War Museum, National Gallery and National Portrait Gallery during the past few days in London, they all have free admission. But they shake you down at every opportunity with prominent donation boxes and a notice suggesting a five pound donation. At the Science Museum there was a single narrow entryway with a staff member upping the pressure to donate by their presence. That's in addition to charges for special exhibitions, opportunities to buy at the Museum shops and to join Friends organizations.
The sole exception was the British Library. It was the only one where I actually paid to enjoy a special exhibit - Shakespeare in Ten Acts - just opened and well worth seeing.
As with the British Library and TNA (the UK National Archives) you won't find donation boxes with suggested amounts at the entrance to Library and Archives Canada.
Both the British Library and TNA have cafes, book and souvenir shops to supplement funding. While I'm sure LAC would provide those facilities if the space allowed, that it doesn't is something for which successive Canadian governments are culpable. That doesn't mean LAC won't gladly accept your donation. Find out how to donate to LAC.