I have seen some people write л like a triangle with the bottom line missing. Is this considered an equally acceptable way to write the letter, or is it considered sloppy?
It is the prototypal shape of that letter (it comes from the Greek letter Λλ).
Russian Л is only written as a trapezoid in printed fonts—which is a bit like lowercase "a" or "g" only using their complicated shape by typefaces, while in writing a simplier outline is preferred.
Yep, this is how it is written. I believe some fonts also have a shape more like what you described, with pointed top rather than л shape.
The Д you can write like a triangle with legs.
Note that written printed format is slightly different to cursive.
That's used sometimes in printed Russian too. Another thing you'll see sometimes is Δ instead of Д.
Here is a selection of how the Cyrillic looks in various typefaces. Only a really Grotesque geometric one will have a triangle for Д
I've seen it quite a few times, but often it was in really grotesque typefaces. I'll see if I can find some of them again.