An efficient and easy-to-perform method was developed for immobilization of CaLB on mesoporous aminoalkyl polymer supports by bisepoxide activation. Polyacrylate resins (100–300 µm; ~50 nm pores) with different aminoalkyl functional groups (ethylamine: EA and hexylamine: HA) were modified with bisepoxides differing in the length, rigidity and hydrophobicity of the units linking the two epoxy functions. After immobilization, the different CaLB preparations were evaluated using the lipase-catalyzed kinetic resolution (KR) of racemic 1-phenylethanol (rac-1) in batch mode and in a continuous-flow reactor as well. Catalytic activity, enantiomer selectivity, recyclability, and the mechanical and long-term stability of CaLB immobilized on the various supports were tested. The most active CaLB preparation (on HA-resin activated with 1,6-hexanediol diglycidyl ether—HDGE) retained 90% of its initial activity after 13 consecutive reaction cycles or after 12 month of storage at 4 °C. The specific rate (r_flow), enantiomer selectivity (E) and enantiomeric excess (ee) achievable with the best immobilized CaLB preparations were studied as a function of temperature in kinetic resolution of rac-1 performed in continuous-flow packed-bed bioreactors. The optimum temperature of the most active HA-HDGE CaLB in continuous-flow mode was 60 °C. Although CaLB immobilized on the glycerol diglycidyl ether (GDGE)-activated EA-resin was less active and less selective, a much higher optimum temperature (80 °C) was observed with this form in continuous-flow mode KR of rac-1.