The simple answer is to do the following steps:
Install El Capitan
Purchase Server.app 5 and install
Run Server.app 5 to upgrade services
However, life is rarely that simply. What services are you running on the current server? Start there. Get a list to understand what services and third party tools you have on the machine (FileMaker? Rumpus?). Ensure that you patch those tools for compatibility.
Check your hardware to make sure it is compatible. Systems running 10.7 may be dropped from support of El Cap. OS X El Capitan - Technical Specifications
Next, plan to make a complete backup of the server to provide a regression path. This may require the purchase of a hard drive. To get the cleanest possible backup of the server, boot the machine from another drive and use Disk Utility to capture the entire drive to a DMG. Dump your users in OD using either a OD archive or exporting to flat files. Make sure you are at 10.7.5 before attempting the upgrade.
Depending on which services you have, temporarily disable firewall port forwards. This will prevent services from connecting before you are ready to permit them to. Also, keep your users off the network as much as possible. Turn off all possible services before upgrading. This too will prevent unexpected access.
Plan time accordingly. Expect at least 3 hours for the upgrade. Download El Cap anytime in advance. The upgrade of the OS will likely take an hour (maybe more if you have old hardware). Expect multiple reboots as you may be applying firmware updates. Then the migration of Server will take 10 to 30 minutes depending on services and possible problems.
Bring one service on at a time and validate function. Start with the foundation services like DNS, DHCP, and OD. Then work out to client services like file sharing, profile manager, etc.
Know what you will be missing after the upgrade. No Workgroup Manager. MCX mostly dead. System Integrity Protection.
Be smart, plan it out. Think it through.
Reid
Apple Consultants Network
Author "El Capitan Server – Foundation Services" :: Exclusively available in Apple's iBooks Store
Author "El Capitan Server – Control & Collaboration" :: Exclusively available in Apple's iBooks Store
Author of Yosemite Server and Mavericks Server books