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The electron-impact ionization of lithium-like ions C3+, N4+, O5+, Ne7+, and Fe23+ is studied using a combination of two-potential distorted-wave and R-matrix methods with a relativistic correction. Total cross sections are computed for incident energies from 1 to 10 times of ionization energy and better agreements with the experimental results are obtained in comparison with the theoretical data available. It is found that the indirect ionization processes become significant for the incident energy larger than about four times of the ionization energy. Contributions from the exchange effects along the isoelectronic sequence are also discussed and found to be important. The present method can be used to obtain systematic ionization cross sections for highly charged ions across a wide incident energy range. [ABSTRACT FROM AUTHOR]