Unfortunately there really isn't anything that tastes like vinegar except for vinegar, and the lemon juice you're trying is about as close as you're going to get.
It just comes down to chemistry. Most categories of edible compounds, like starch, protein, hydrocarbon lipids, etc. have a ton of different compounds in them, so if you have to avoid one you can often find another with very similar characteristics regarding flavor and how it reacts with other compounds when being cooked. These chemical similarities are what allow for good substitutions.
The problem is that vinegar comes from the much less human-friendly compound category of acids. The list of edible acids is incredibly short, and once you rule out the ones you either can't use (carbonic only exists in carbonated drinks) or wouldn't ever want to put in your mouth (butyric and lactic come from spoiled dairy products), you only have a handful of possibilities. The food acids you're left with at this point are:
- oleic (olive oil)
- palmitic (palm oil)
- oxalic (tomato)
- tartaric (tamarind)
- citric (citrus obviously)
- acetic (the vinegar you're trying to get away from)
The only thing on that list that even remotely shares vinegar's tanginess is citric acid, which is why lemon juice is the standard suggestion to use in a pinch if one is out of vinegar.
Your best bet would be to experiment with other citrus juices and see if perhaps using something other than lemon would help things taste better.