As a borough, Lewisham's offerings seem woefully few, but Deptford and environs has some notable opportunities to visit buildings which should not be missed, as well as a few walks.
Deptford Town Hall on New Cross Road is open on Saturday, 10am till 5pm and offers "lavish, nautically-themed baroque features" both inside and out.
Have a nebby* behind the great black gates of the Master Shipwright's House on Watergate Street - open Saturday 10.30 till 5 and Sunday 10 till 2, with promises of re-enactors, tea and cakes, and the presence of the Lenox Project and Sayes Court Garden community groups. The oldest remaining building of the former Royal Dockyard. If you haven't been here before, you'll be gobsmacked at what you've missed. If you have been before, you'll be back for more.
(*northern slang for 'nosey' where I'm from)
If the weekend is clear, there are always great views to be had from the top of the Seager Distillery Tower - certainly one local building where it's preferable to be in looking out. Saturday 10-5 and Sunday 10-1. There's usually a short wait to enter, as there's a limit on numbers at the top, but it's worth a look if you want to see Deptford from a different angle.
Walking tours include Sayes Court (pre booking online only), Pepys Park & Surrey Canal Linear Park (meet outside Deptford Park School on Saturday at 11am) and Deptford Town Centre (meet at the north end of the high street outside Boa Lang on Saturday at 2pm).
Despite the lack of places open in Lewisham, Deptford residents have Greenwich and Southwark not too far away so it's worth looking at those parts of the guide if you want something close at hand - and there's plenty a bit further afield that's worth travelling to.
One particular recommendation is the Deptford Creek Swing Bridge (or as the guide would have it, the Greenwich Reach Swing Bridge) where the architects and engineers who designed it will be present on Sunday from 1pm till 5pm. The bridge will be opened on Sunday at 3pm so if you've always wanted to see it swing without being inconvenienced, now's your chance!
Full information is online at http://www.openhouselondon.org.uk