I don’t think that a device in the configuration you want/need can be managed via cAPsman, the radio of the Ax lite won’t be an AP (as seen by the main router Ax2), it will need to be configured as station (please read as “client”) to connect to your current Ax2, then a slave interface will be added as AP to serve your clients.
Since the device has only one radio and it is needed as what is often referred to as “wi-fi repeater” or “wi-fi extender” half of the time it will transmit/receive to/from AP and the other half to/from clients, so speed will be roughly 1/2 of the max possible.
Another approach to have better speed (not suitable for your case since you have weak 5 GHz signal) is to use a device with dual radios (such - only as an example - another Ax2) configurinfg the 5 GHz radio as station connected to the “main” Ax2 and the 2.4 Ghz as AP for the clients.
You could try the reverse, having the 2.4 GHz as station and the 5GHz as AP, but then all your clients will need to be 5GHz compatible.
At the end of the day, what is really relevant is the speed/bandwidth you expect from the setup, since you started thinking of a Map Lite, very likely your expectations are low enough, and the single 2.4 GHz radio of the Ax Lite will be enough (in any case it will be roughly 2x faster, being 574 mbps/wi-fi6, than a Map or Map Lite that are 300mbps/Wi-fi4).
As holvoeth suggested, unless your house is very large/has a strange electrical plant[1], a powerline solution should be considered (MOCA adapters, even if you have an unused coaxial would surely go over budget), there are decent powerline adapters (TP-LINK, yes, I know) pairs, one with wi-fi and one without, available for around 70-80 Euros, see this thread:
http://forum.mikrotik.com/t/extend-wifi-in-small-house/183442/1
[1] the issue with powerline adapters is when the electrical plant is multi-phase AND the two sockets you want to connect the devices to are connected on different phases, this doesn’t usually happen in “normal” houses, only in some cases of very large ones (it depends also on the country, if I remember correctly three-phase plants even in small houses are common in Germany), then - see the linked thread - multiphase powerline adapters do exist, but obviously they are not exactly cheap..