Most turf grasses in the PNW will be blends of various cool weather grass seeds, however sod farms seem to prefer monocultures and often go with a single type. Because many of these grasses look virtually indistinguishable from each other, best to go back to the source and ask where you purchased the sod. Because our cool season grasses want to go dormant in summer, I tend to recommend fall as the best time to overseed or do much remedial lawn care. What you can do now is to aerate the soil, using a plug or core aerator. Aerating is one of the best things you can do for a lawn or the ideal first step in lawn care prep. After aerating, spread a thin layer of compost, just a half inch or so. Water as necessary but not too frequently and deeply when you do. In my Puget Sound climate, once every week to 10 days is usually sufficient through summer provided the water penetrates down 6-8 inches. Weed manually as required. Then in fall you can overseed. Again, cover with a thin layer of compost (better than peat or topsoil) and keep moist until full germination, usually about 10-14 days. Mow when the new grass is at least 2.5 inches tall. And you can still fertilize before winter. If you overseed in September, you should be able to fertilize in mid to late October. Of any time of year, the fall fertilizing is the most beneficial in our region. And opt for an organic product if you can.

My first guess would be Virginia Creeper. It's a native vine that creeps along the ground and up into trees and along fences. I usually let it be, I've got worse things to deal with in the garden. In one area I planted native bushes and covered with a thick layer of mulch, Virginia Creeper quickly took over and made a nice looking ground cover, choking out the weeds.

No grass will thrive in shade. However, by the looks of your photo, like you have grass that has been established there ... It's just been abused and it's also not quite the spring growth period yet. You could look at options to reduce the shade, eg raising the tree canopy a little bit to increase the sunlight (and air flow.). But I'm willing to bet your real enemy is soil compaction + turf stress both caused by the lacrosse abuse. Rye grass loves sun. It won't thrive in shade but that's ok. Your challenge is getting something to grow there that will prevent it from going completely barren; nothing will thrive with constant abuse. If you cover the area up, you risk "damaging" the soil by blocking sunlight and water. Plus, I would imagine it would be more likely that someone could trip or slip on whatever it is that you are putting down. Another option is to just let it be. In the fall, reseed the area with Turf Type Tall Fescue. That does better in shade than Rye Grass and Bluegrass. Another option is to buy some sod and roll it out after lacrosse is over. You wouldn't want to put sod down while they are practicing because it needs time to settle and dig in to the soil. You also would need to keep off it for a period of time and keep it well watered (and fed) to encourage this. Another option is to just give up on grass there and go a different route, eg groundcover, mulch or gravel. But where's the fun in that? Personally, I would go with my original idea. Regularly throw down Perenniel rye grass during lacrosse practice while separately growing some more desirable turf (eg bluegrass or turf type tall fescue) in some pots to plug in later.

Just get straight glyphosate - it doesn't have to be RoundUp specifically and there are less expensive brands of this herbicide on the market (Ferti-lome sells a product called Killzall that is less than half the price of the equivalent concentration and size of RoundUp). If you do go with the RoundUp, just select the Weed and Grass Killer - no need for any other additions to the mix. As I noted previously, you may very well need several applications and it is suggested to allow at least 2 weeks after the last treatment before reseeding. And it is too early to reseed - too hot and too dry for most northern, cool season grasses to germinate well. Generally, the ideal time for fall seeding is early fall - September to early October, depending on your specific climate. And any cool season turf grass blend recommended for your area is fine. Most independent garden centers - not the box stores - will have blends that are appropriate for your area.