Tactics for DEFENDING

I think I'm pretty decent at attacking tactics and can spot most of them, but one thing I really want to learn is defending these tactics. I think this is because my brain can now recognise all these tactical patterns, but not when they're flipped the other way round. This means I sometimes lose material because I failed to defend a tactic (usually multiple move combinations), though I'm quite sure I would've spotted the tactic too if I was my opponent.

I haven't heard any other chess site try this, but I think it would be pretty interesting and unique, possibly helpful too.

Thoughts?

Some basic examples would be blocking checkmates, or preventing forks/skewers, or retreating your queen from a dangerous position, or at higher levels even spotting 4 to 5 move combinations from your opponent and playing an appropriate move to defend against that combination.

I agree! All puzzles I've encountered so far start from a winning position, immediately after your opponent missed to spot your winning tactic.
For learning purposes it would be really great if Lichess could also generate some puzzles which start in an equal or even slightly worse position, where you have to find the only "not losing" move.

There is a software program called CT Art (Chess Tactics Art currently on 6.0). It's not free, but it's effective. For most problems, after solving, it flips the board, keeps the position, but changes whose turn it is. It's a great way to learn that defensive tactics. I don't work for them or anything like that, but if you're interested in getting it, here's the link to the shop I got it from.
http://chessok.com/shop/index.php?main_page=product_info&products_id=709

(If mentioning another website like that is against Lichess' rules, I can edit my post to remove the link)

There are some really, really high rated puzzles on lichess that involve defensive tactics. I saw someone complain about it in another forum because it was a mate in 7 for the other side and you had to survive 7 turns. These puzzles may have been "bugged" since I didn't see them often.