@LB99 is steering you in the right direction.
The Phillies will be playing in Atlanta on Saturday, and it does not appear that there are concerts scheduled for Citizens Bank Park this weekend. There is nothing scheduled at the Wells Fargo Center. The NCAA Men's Lacrosse Championships are at the Linc. In short, the parking lots for all three facilities will be open for parking for the LAX Championships, so you should have no problem getting to the Linc, and no problem parking for the PSU LAX semifinal on Saturday.
While there is a lot of public transportation in the Philadelphia region, it's not a great option for the Linc. Coming from Harrisburg, here's what you'd have to do to use public transportation:
1. Get off the PA Turnpike at the Downingtown exit (Exit 312)
2. Take PA 100 South for @ 5 miles (give or take) to the Exton train station
3. There, get on the Paoli/Thorndale line toward Philadelphia
4. Unfortunately, on Saturday there is a very limited schedule from Exton. There is a train at 6:46 am, and the next one is at 10:46 am. Alas, it takes an hour to get to Suburban Station in Philadelphia, which means the 6:46 am train is pretty early for you, and the 10:46 train is not going to get you to the game until after it starts
5. A work around to the issues taking the train from Exton is to proceed on the Turnpike to Exit 320
6. Take PA 29 south, and use a GPS to get to the Malvern train station
7. The Malvern station is on the Paoli/Thorndale line, but it has full service on Saturday
8. There is a train every hour in the morning at the 51 minute mark (i.e., 5:51 am, 6:51 am, 7:51 am, etc.)
9. You'll want to take the 8:51 am or the 9:51 am train. The 10:51 am train is the same train as the Exton 10:46 am train, and it will not get you to the game on time
10. Assuming you wish to take the train (and I strongly suggest you just drive to the Linc), you'll take the 8:51 am or the 9:51 am train to Suburban Station. Those two trains will get you to Suburban Station at 9:45 and 10:45 am respectively.
11. Once you get off the train, you'll want to follow signs for the Broad Street Line. Basically, you're going to have to transfer from the train to the subway
12. When you get to the subway (and you'll have to pay a new fare), you'll want to take it South, to the NRG Station
12. The subway runs every 10 minutes, and it takes @ 14 minutes to get from City Hall (the stop you'll be walking to, underground, when you exit the train at Suburban Station) to the NRG Station
13. Once you get off the subway and up to the street level, just follow the crowd to the Linc. (Basically you'll be turning left out of the station, walking a couple of blocks, and then turning right to get to the Linc.)
14. Repeating what I said in the above #10, I strongly suggest that you drive to the Linc and park there. However, if you really are set on using public transportation, the above info is your best bet for getting to the Linc when driving in from the Harrisburg area.
Good luck