Do you mean a grammar with left and right recursive rules, or a single production rule with left and right recursive alternatives?
If a single production rule is both left and right recursive, the grammar is ambiguous. For example, the following rule
$A \to \alpha A \mid A \alpha$
has the following two (left-most) derivations:
$A \Rightarrow \alpha A \Rightarrow \alpha A \alpha $ corresponding to the grouping $(\alpha (A\alpha)$
$A \Rightarrow A \alpha \Rightarrow \alpha A \alpha $ corresponding to the grouping
$((\alpha A) \alpha)$
But a grammar can have left recursive and right recursive rules in different production rules and that can be unambiguous. For example, the following grammar:
S &\to X \mid Y \\
X &\to X b \\
Y &\to a Y \\
In this grammar, $X$ and $Y$ are left and right recursive, respectively, but the grammar is unambiguous.