I'd recommend replacing the entire battery pack at once. The way it will behave with different ones in series, especially some old and some new, is unlikely to be the way you'd like it to, although it will probably still operate.
That said, you can connect any batteries in series...but with some behavior notes and cautions about stuff in series:
The lowest Ah (capacity) battery is the maximum Ah you can pull from the system. Because lead-acid batteries only supply about half (or less, as they age, often much less) their rated capacity in EV traction use, that's probably going to be your limitation.
The lowest A (amps) rating, or ability to deliver current, battery is the maximum current you can pull from your system.
Any pack protected by a BMS must have discharge FETs on it that are rated for the full voltage of the ENTIRE series string of packs, or the FETs will probably fail as soon as that BMS detects any issue (including normal LVC) within it's own pack and turns off the output to protect it. This is becuase you get full voltage across any open connection in a series string of connections, and that's what a BMS turning off does, is open the connection.
FETs often fail shorted, so the discharge FETs could fail stuck on, and the pack would then continue to drain, overdischarging if it was near empty, or overheating if it was getting too hot, etc.; the BMS would no longer ever be able to turn off the output. A secondary concern is that FETs failed in this mode have higher resistance than when working, so they heat up more and you can end up with further failures, up to and including a fire if something touching them is heated enough to ignite. (including cells). A more primary concern is that the cells themselves can be damaged even up to causing a fire by the overdischarging/etc that can happen in this BMS failure mode.
(the charge input is a separate set of FETs affected by what you do with charging).
Because you have different packs with different capabilities and different amounts of voltage sag per amp drawn thru them, the system performance will be different than before (better or worse, depending on actual pack characteristics), and the system battery meter (probably a 3-LED type; they're common, but same applies to any other style of meter other than actual voltmeter) won't be accurate because the voltage range and response of the different packs will make the total range and response different.
If you have a wattmeter on the system that gives you a total Ah used readout, you can use that as a guide for when to stop, based on whatever the lowest-capacity pack is in your series string.
