Why does Ricardian Equivalence not hold when there are different borrowing and lending rates on the market? If you can propose any explanation (intuitive, graphical or algebraic), I will appreciate it
Barro helped define Ricardian equivalence, wherein one of the assumptions was that the capital market is perfect(can lend and borrow at a single rate). 
so it can be easily inferred that Ricardian equivalence does not hold true when borrowing and lending rates are different. 
and while it is assumed under Ricardian equivalence that consumers are able to save/ spend according to tax regimes, it is debatable, as was mentioned by Ricardo himself, that people may have a myopic approach towards tax regimes. 
although it holds credibility in some specific examples, the discounting of one of its basic assumptions can be the reason for it not holding true when borrowing and lending rates are different.

it would be more helpful if you could elaborate on the type of examples/statements you want to support your answer.