Are you sure the power supply you swapped in is compatible with the Lenovo H50-55 motherboard? Some manufacturers' pre-built systems use proprietary power supplies with different wiring than the ATX standard, and it could be that you need a specific PSU that works with that motherboard in order to pwoer it up. If you have a power supply specifically for the Lenovo system, you could give it another try with that and see if the computer will power up. If that works, back up all of your valuable data from the computer. Before you do that, though, you may wish to pull the motherboard out of the computer and carefully inspect it with a good quality flashlight held directly overhead, looking for any signs of damaged (blackened or burst component tops). You can also give it the "smell test" to see if there's anything which smells burnt. Start your investigation around the PSU connector.
It may be possible to salvage some parts from the computer like the CPU, the RAM and the drives, and they may continue to work for some time without error, however, the kind of damage that is done inside a computer chip from ESD, nearby lightning strikes, and so forth over time is cumulative, so they shouldn't be considered reliable. They may be "good enough" for a back up/secondary computer, though.
Like @securitybreach, I have had good results with CyberPower UPSes. APC are good, too. Keep in mind that a UPS is not going to protect you from a nearby (or a direct) lightning strike. You have to physically unplug things. Even your UPS.
Back in the mid 1990s I was working in Woodland Park, Colorado at a software company that was in a strip mall. The first floor was filled with all sorts of tourist stores, and they had 50 metal flag posts (one for each state) in their parking lot as a kind of a "draw attention for the tourists coming through" kind of thing. Surprisingly, it was a couple of years before we had a strike on our building, but we eventually did. The flash and the boom from the lightning and the thunder occurred at the same time, and the building shook as if a truck had run into it. All of the UPSes tripped--some survived, others needed to be replaced, and we lost a lot of switch ports in our server room, network cards in PCs throughout the building, etc. A few days later, one of the network guys gave me a short 6" tube of PVC conduit they had to cut out. Welded into the bottom was an Ethernet cable whose jacket had melted into it.
Right now, I'm staying about four or five miles away from where Nikola Telsa built his Experimental Station to study lightning. When there's nearby lightning strikes, I power down my electronics, unplug the UPSes and power strips from their respective AC outlets, and unscrew the coax cable from my modem. I lost one computer the first year I was here, so that was my own expensive lesson. For a while, the power company out here offered the installation of a whole-home surge surpression service, which required shutting off the power to the building for installation, but they no longer offer the service. You might want to check and see if your power company offers something like that.