In this article, we construct the six-quark currents with the $J^P=0^+$, $0^-$, $1^+$ and $1^-$ to study the $Lambda_c$$Lambda_c$ dibaryon and $Lambda_c$$bar{Lambda}_c$ baryonium states via QCD sum rules. We consider the vacuum condensates up to dimension 16 and truncation of the order $mathcal{O}(alpha_s^k )$ with $kleq3$. The predicted masses are $5.11_{-0.12}^{+0.15}$GeV, $4.66_{-0.06}^{+0.10}$GeV, $4.99_{-0.09}^{+0.10}$GeV $4.68^{+0.08}_{-0.08}$GeV for the $J^P=0^+$, $0^-$, $1^+$ and $1^-$ states, respectively, which can be confronted to the experimental data in the future considering the high integrated luminosity at the center-of-mass energy about $4.8,rm{GeV}$ at the BESIII. We find the terms with $frac{3}{2}< k leq 3$ do play a tiny role, and we can ignore these terms safely in the QCD sum rules.
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