Spoke tension won't do much for lateral-stiffness (unless the wheel was SUPER loose to begin with). The factors that determine lateral-stiffness are:

1. flange-width, the wider apart the flanges and the larger the included-angle, the more stiff a wheel. This is by far the biggest factor in lateral-stiffness

2. rim-stiffness. Before building a wheel, bend the rim by hand, press on it against the ground to make it an oval. You'll find that there's a big difference in raw rim-stiffness. However lateral isn't the same as vertical stiffness and the actual amount of force required to bend a rim by hand is minimal. Most of the stiffness comes from the spoke-angle.


However, what are you using to measure your wheel's lateral-stiffness? Because on-bike "feeling" of stiffness is an awfully inaccurate instrument. Tyre-deflection is typically 10x more than rim-deflection and pressure-adjustments are very noticeable. And the acoustics of different rims give different impressions of stiffness as well.

BTW, the fork-flex is easily 10x more than the wheel-flex anyway. And QR stiffness makes a different as well. You can totally tell the difference between a QR with steel versus titanium axle in how much the rim hits the brake-pads in out-of-the-saddle sprinting.