In general, you can put lime down anytime, assuming what your talking
about is limestone type, not some fast acting product. It takes a
very long time for limestone to react with the soil.
In this case, though, the weed and feed products generally rely on the
product sticking to the leaves of the weed. So, I'd do the lime first
so it doesn't knock off the weed/feed. And use the pelletized type of
lime. If you use the pulverized/powdery type, it will leave the
weeds coated.
If it were me, I'd put down the lime, followed by fertilizer with pre-
emergent crabgrass control, and use a tank type sprayer with a
herbicide to address the weeds. The tank allows you to deliver it
right to the weeds, is more effective, and uses less herbicide, which
is better for the environment.
The other thing to consider is if the lawn is in really bad shape, it
may be better to just get through this season and do a complete kill
and renovate in Sept. If you have mostly weeds and some crappy/
undesirable grass, it could be more work and trouble trying to salvage
it, as opposed to starting over with a good quality grass.
Lime can be put down anytime. I do both the same day.
It is better to post a question just once.
The weekend was passing by and he needed an answer quick!
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Art