Edit: I might have jumped the gun a little. Unfortunately, XDA often groups up roms by device model series, not exclusive models. It would seem that the highest custom ROM available for your model that is stable and working is Android 4.4.
My honest suggestion would be go here:
https://forum.xda-developers.com/lenovo-a3000
Make an account and post asking about updating. The folks at XDA are really good and should be able to guide you through rooting the device.
The process is not hard, but it is messing around with key components of your device and if you are careless you could turn it into a paperweight. Follow this guide at your own risk. Make absolutely certain you are using stuff designed for your SPECIFIC MODEL of tablet. Close isn't good enough, it has to match. It basically comes down to the following steps:
ALWAYS MAKE A DATA BACKUP FIRST.
1. Go into Settings -> About Device -> Tap on ... Build number (you can kind of just test it, but I think it's build #) 7x. You should get a toast saying that you're about to enable developer mode. Continue until you do.
2. Go back into settings root. Settings -> Developer Options -> Enable USB Debugging
3. Download "Minimal ADB and Fastboot" (google it) and install. I would suggest adding the folder to your path variable.
4. Download a custom recovery (I would recommend TWRP) available via XDA. Someone will link you if you ask, and I think I saw one.
5. Download a custom ROM. Cyanogenmod is a big name with a good reputation. I'd suggest them if you can find it. You'll want to ask what's available - keep in mind that
you need to ask and receive positive validation that it will work for your SPECIFIC MODEL #. While the devices share a serieis, they may have different hardware or small differences, and that's no good if you're trying this.
6. Check that you have an adb connection with the device. Hook it up to your computer, open adb.exe and type "Adb devices"
You should either see something listed, or get a prompt on your device screen to enable connections from that computer. Make sure your USB setting is set to MTP, not charge only.
7. If you get such a connection and allow it, type: "adb.exe reboot bootloader" and the device should restart into a minimalistic dos-like menu.
8. Type "fastboot oem unlock" (unlock the bootloader - you may need to use another method to do this. Follow the XDA guides over what I've typed here)
9. Note: this will erase your data I believe, so ensure you've got that backup made before this point.
10. Type "fastboot flash recovery <recovery image file you downloaded. Should have an extension of .img"
11. DO NOT DISCONNECT YOUR DEVICE. MAKE SURE YOUR POWER AND CABLE IS RELIABLE BEFORE THIS POINT.
12. Power the device on using the button combination to get into recovery mode (or do the adb trick I mentioned earlier once the device has turned on normally, but type "recovery" instead of bootloader)
12. Once you have a custom recovery installed and booting, make a TWRP backup. See XDA for instructions on how to do that. Google probably will as well. It's not hard.
Excellent. Now, follow the root guide that is on XDA. Basically, you should put the rom zip on your device, and then go "install from zip" in the TWRP menu. If all goes well, it may take some time to boot (the first time) but eventually you should come to a setup screen. Follow that per usual, and enjoy using the unit on the new OS.
It's worth noting that a lot of stuff in newer Android versions is basically taken from FOSS community projects like Cyanogenmod.
But yea - XDA is really the place to ask about this.