Recommend a sustainable weekly training schedule that includes weights
 

I'm cat 3 and want to continue to have fun and be competitive as a cat, no real need to upgrade. I want to have a sustainable schedule that incorporates powerlifting/olympic lifting, because I enjoy it. I want to race once/week, either Sat or Sun obviously.

Previously, I did Monday off, T/W/Th bike, Friday Z1, Sat/Sun big ride or race.

Really just looking for a # of days on-bike I need to do to maintain, slowly develop my engine?

Over the winter I was lifting heavy twice a week, on Monday & Thursday, and riding the other days. I take a polarized training approach on the bike, so a couple interval/race days a week and the other days in zone 2. This worked out well for me. During the racing season, the Thursday workout switches from heavy lifting to a speed/power emphasis (power snatches, some one-legged work, kettle bell swings, etc). On weeks when I want to be fresher for an important weekend race, I skip the Thursday weight workout and either rest or do an easy day on the bike (usually the latter).

So my schedule would usually look like this.

Monday - weights, heavy
Tuesday - zone 2 ride
Wednesday - interval workouts. Either a longer one after work, or doubling up with a short workout on the trainer at lunch and an outdoor workout after work. May include a weekday crit if there's one available.
Thursday - weights, speed/power workout; or active rest if important race coming up.
Friday - zone 2 ride
Saturday - road race or long group ride with a mix of intensities.
Sunday - road race or some other type of ride, usually with some sweetspot/threshold work.

So most weeks that ends up being 5 days on the bike, but some of that is pretty easy. Total time is usually in the 8-10 hour range for the bike and another 2-4 hours in the gym.

I think your attention to a schedule is good factor in any development program. However, your schedule can only work when you account for the "life stress" you sustain from work, family and other interests.

For good health your training, like your personality - depends on successful integration of all your activities.

I wouldn't recommend using either powerlifting or Olympic lifting to improve your cycling. IME using a specific weights program which improves cycling works. Not much else does. If you just want to have fun in the gym and don't care about the cycling, that's another matter.

Be that as it may, with twice a week one gets improvement. With once a week one holds steady. Therefore the usual prescription is 2-3 times a week in the pre-comp period, i.e. winter base, then once a week during comp season.