Multiclassing Lore Bard and the Magical Discoveries feature. Can they access 4th level spells?

Level 6: Magical Discoveries

You learn two spells of your choice. These spells can come from the Cleric, Druid, or Wizard spell list or any combination thereof (see a class’s section for its spell list). A spell you choose must be a cantrip or a spell for which you have spell slots, as shown in the Bard Features table.

You always have the chosen spells prepared, and whenever you gain a Bard level, you can replace one of the spells with another spell that meets these requirements.

A bit in doubt about this feature of the Lore bard.

Can a Paladin 1/Lore Bard 6 take Conjure Minor Elementals and Greater Invisibility? They have 4th level spell slots. Or it must be Paladin 1/Lore Bard 7?

The text says "as shown in the Bard Feature Table", but that does not mean that a multi class could not have level 4 spells as well by that point. Meaning, is "as shown in the Bard Feature Table" a necessary or sufficient condition for a level 4 spell like CME and Greater Invisibility?

No, they can't. "As shown in the Bard Features table" is pretty clear, I think.

Also note that the multiclassing rules say that you prepare your spells for each class separately as if you didn't have any other classes. I don't see anything in the Bard features that suggests the intent is for this feature to work differently.

Here is the part that I do not understand well: spell slots and spells prepared are two different things right? The description does not say   "A spell you you choose must be a cantrip or a spell of a level that you can prepare". It says "A spell you choose must be a cantrip or a spell for which you have spell slots".

Sure, "As shown in the Bard Features table" brings attention to the fact that a bard needs to be lev 7 to have a 4th level slot, but that does not necessarily mean that a multiclassing character might have such level 4 slots already available from multiclassing. 

Also the feature let's you learn a spell from a completely different class for which you definitively have not any preparable spell already. 

I am not married to the idea, but I really think the wording is confusing.

Spell Slots. You determine your available spell slots by adding together the following:

• All your levels in the Bard, Cleric, Druid, Sorcerer, and Wizard classes
• Half your levels (round up) in the Paladin and Ranger classes

This table might give you spell slots of a higher level than the spells you prepare. You can use those slots but only to cast your lower-level spells. If a lower-level spell that you cast, like Burning Hands, has an enhanced effect when cast at a higher level, you can use the enhanced effect as normal.

For example, if you are a level 4 Ranger / level 3 Sorcerer, you count as a level 5 character when determining your spell slots, counting all your levels as a Sorcerer and half your Ranger levels. As shown in the Multiclass Spellcaster table, you have four level 1 spell slots, three level 2 slots, and two level 3 slots. However, you can’t prepare any level 3 spells, nor can you prepare any level 2 Ranger spells. You can use the spell slots of those levels to cast the spells you do prepare—and potentially enhance their effects.

Spells Prepared. You determine what spells you can prepare for each class individually, as if you were a single-classed member of that class. If you are a level 4 Ranger / level 3 Sorcerer, for example, you can prepare five level 1 Ranger spells, and you can prepare six Sorcerer spells of level 1 or 2 (as well as four Sorcerer cantrips).

Each spell you prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell.

All I can tell you is that I think it's very clear from the way both things are worded that the intent is that multiclass characters do not get access to higher level spells just from having higher level spell slots, and if the intent was for Magical Discoveries to override that principle, it would be called out somewhere explicitly.

The fact that "as shown on the bard feature table" is included in the text of magical secrets means that the spell slots must in fact be shown on the bard feature table. Multiclass spell slots are not shown on the class feature table.

whenever you gain a Bard level, you can replace one of the spells with another spell that meets these requirements.

If I understood it correctly, a Lore Bard 7 can pick Greater Invisibility though right?

Quote from Jayce_Danathar >>

If I understood it correctly, a Lore Bard 7 can pick Greater Invisibility though right?

That's correct -- they have 4th level spell slot (as shown on their features) and can thus replace one of the spells they learned at level 6 with a 4th level spell.