I usually default to lifting 2X a week from December through early March, then 1x a week during the rest of the season, with several breaks of 2-3 weeks to recover. (I'm referring to lower body weight lifting. I don't change upper-body/core lifting routines for cycling.) I either don't ride on lift days or ride right after lifting. This is mostly due to time constraints. This winter, for example, I've been lifting mostly on Tuesdays and Thursdays, with a 30-45 minute, low power ride on Wednesdays (e.g. - cadence/form drills), and longer, Z2/3 rides Saturdays and Sundays. If time allows, I might add another easy ride right after lifting. I'm about to shift to lifting only one day and adding another hard, interval riding session during the week. If the gods permit it, this is also the time of year I may try for a high volume week where I ride as many days as I can for as many hours as I can. I don't lift at all during such a week; the sole purpose is to increase endurance/FTP.
While performance gains can be difficult to measure with precision, much less attribute to any one training thing, I do find that lifting regularly makes rollers/short hills much easier from a perceived effort standpoint. It also helps my top-end power, but since I'm not a sprinter, that doesn't translate to much in actual races. On longer climbs or the flats, I'm not sure I notice a difference. But I'm not just lifting for cycling. At 53, I'm mindful of maintaining bone density, ligament strength, etc., which a low-impact sport like cycling might not provide as well as other exercise.