The quickest way would be to take Métro line 6 towards Nation, alight at Bercy and walk along rue de Bercy. Gare de Lyon is visible from Bercy Métro.
However, if you're keen on avoiding the Métro after last time, you can take bus 91. The most difficult thing is locating the very poorly located bus stop. When you leave your TGV, you must leave via Hall 2 (on the top floor) and exit via the 'Jardin Atlantique'. The escalators from the platforms to Hall 2 are half-way along the platforms (i.e. do not go towards the front of the train when you arrive, that is Hall 1). If you arrive at Vaugirad (Hall 3) on an Intercités/OUIGO, then you'll have to go along platform 24 and access Hall 2 that way. When you get to Hall 2, find the signs for bus 91 and follow them (they'll direct you to stairs/lift to street level). It also stops at the bus station at the front of Montparnasse but your chances of getting a seat there are much lower and it's a longer trek with luggage.
The bus stops right opposite Gare de Lyon, much easier. It completely depends on the traffic this way, could be 20-30 mins, could be 50. If it's midday I'd say around 30.