There is no lift access to any platform at Baker Street (there are though escalators to all platforms, my view from your description of the situation is that you'd want to avoid these as well but if you feel you could use them then your original route would be fine). There is lift access at Liverpool Street station but only to the eastbound Circle, Hammersmith & City and Metropolitan (the central line has loft access in both directions).
This leads us to possible alternatives, my personal view is that in your wife's situation id also be minimising the total distance I'd want to walk but she already feels capable of walking to Baker Street. You haven't given an exact address, but if you feel your wife could walk a little further to Paddington station she could board an eastbound Circle or Hammersmith & City line train to Liverpool using only lifts.
If your wife feels unable to walk to Paddington Station might she still be able to manage the likely nearer Marylebone Station? There are no direct trains from here to Liverpool Street, she would have to take a Chilton service to Chorleywood, before boarding a Metropolitan line service back to Liverpool Street. While this route has the least amount of walking and steps, it adds a considerable detour taking around 2 hours.
Have you also considered using buses, pushchairs can be placed on London buses provided the space is vacated for a wheelchair passenger should one arrive. The 205 bus runs every 6-10 minutes during the peak and links Baker Street to Liverpool Street.
Sources and potentially useful information:
Information on steep free access including a download link for a map showing which stations have lift access (avoiding stairs tube guide): https://tfl.gov.uk/transport-accessibility/wheelchair-access-and-avoiding-stairs#on-this-page-0
This journey planner has an option under preferences for step free access: https://tfl.gov.uk/plan-a-journey/
205 bus timetable: https://tfl.gov.uk/bus/timetable/205?fromId=490000011D
Information about using your buggy: https://tfl.gov.uk/transport-accessibility/getting-around-with-your-buggy?intcmp=41227
The Station Master app (not affiliated) offers 3D maps of most stations that you may find useful. You'll need to buy the app to get all of them but they do have Liverpool Street, Baker Street and Paddington available as free samples on their website.
This site also contains 3D maps of some tube stations.