Multicollinearity means that your predictors are correlated. Why is this bad?
Because LDA, like regression techniques involves computing a matrix inversion, which is inaccurate if the determinant is close to 0 (i.e. two or more variables are almost a linear combination of each other).
More importantly, it makes the estimated coefficients impossible to interpret. If an increase in $X_1$, say, is associated with an decrease in $X_2$ and they both increase variable $Y$, every change in $X_1$ will be compensated by a change in $X_2$ and you will underestimate the effect of $X_1$ on $Y$. In LDA, you would underestimate the effect of $X_1$ on the classification.
If all you care for is the classification per se, and that after training your model on half of the data and testing it on the other half you get 85-95% accuracy I'd say it is fine.