Lest now takes only a bare infinitive

Yes, there is a “rule”: in Present-Day English you should ignore the main clause and always use the bare infinitive after lest. That’s what everybody else does even in literary English. So if you don’t follow this rule you’d risk confusing people with something that they would quite likely find ungrammatical.

In days of old...

But it was not always this way: up until around a hundred years or so it was perfectly easy to instead find past subjunctives there when the matrix clause itself was in a past indicative.

I believe the reason this changed from how it used to be done in English is because we stopped perceiving the verb in the subordinate clauses governed by lest as a verb that had both tense (past-vs-present) and mood (indicative versus subjunctive). It was this understanding of tense and mood together which in olden days allowed us to vary the tense while holding the mood constant.

Now instead of being an inflected present subjunctive, it is perceived to be an untensed infinitive with the zero-modal. So you can no longer change its now-nonexistent tense to match the main clause’s tense as was once our habit in the literary English of an earlier age.

So no matter what you do with the poor verb in the first clause, the bare infinitive in the second clause following lest remains inviolate: Don’t mess with it.

Details

This is the same thing that occurs with the so-called mandative subjunctives, and for the same underlying reason.

1. His mother insists that he wash the dishes beforehand.
2. His mother has insisted that he wash the dishes beforehand.
3. His mother is insisting that he wash the dishes beforehand.
4. His mother insisted that he wash the dishes beforehand.
5. His mother was insisting that he wash the dishes beforehand.
6. His mother had insisted that he wash the dishes beforehand.
7. His mother would have insisted that he wash the dishes beforehand.
8. His mother will have been insisting that he wash the dishes beforehand.

That's because that bare infinitive is itself a modally marked form in that it already carries the zero modal, if you would. Deviating from that causes it to lose its modal meaning.

That’s why we never touch what was once a present subjunctive.

At least, today we do not. Once upon a time, a preterite form in the main clause demanded a preterite form in the subordinate clause, even here:

• c1450 Seven Sages of Rome 2658
  Seven clerkys were in Rome And holpen for to take game ... That the city were lookyd aryght.

However, English has changed since then. Now we do not inflect into the past subjunctive for those sorts any longer:

• 1923 Sherwood Anderson, Many Marriages, 3
  He was ... inclined to have dreams which he tried to crush out of himself in order that he function as a washing machine manufacturer.
• idem 241
  She ... kept putting up the hand that held the stone, first closing it carefully that the previous be not lost.

Those two examples are from page 864 of the second volume of F. T. Visser’s monumental An Historical Syntax of the English Language.

Visser has more to say about this new trend in the context of lest:

752―Quite recently writers have begun to use the futural present in clauses opening with the conjunctions lest and on (the) condition that in spite of the fact that the main syntactical unit has the verb in the preterite. More instances are given in the sections on the modally marked form. (§ 878 s.v. lest end paragraph).

• 1909 J. L. Allen, Bride of the Mistletoe p. 161, With noiseless steps lest she awake him, she began to move about the room
• 1940 Wodehouse, Quick Service (Penguin) 22, Loath though he was to encourage his employer in any way lest he get above himself, Joss was forced to drop a word of approval.
• c1929 Susan Ertz, Madame Claire 291, Madame Claire agreed to this, on the condition that when she came for him again at six, she stay for half an hour (J.)

And here is what he has to say about it in the section 878 he just referenced:

878―Types

• ‘nyle ȝe deme, that ȝe be nat demyd’ ^{(tchrist: that's in Old English)}
• ‘hine mod geband þy læs he on niht onweg fluge’ ^{(tchrist: that's in Middle English)}
• ‘They are anxious to be rid of him lest worse befall’ ^{(tchrist: that's in Modern English)}

These final clauses with modally marked form of the verb differ from those discussed in the preceding section in that they express negative intended result. They are introduced by þæt not, that not, þy læs (þe), enaunter, læs þe, læste, leaste, lest.¹)

The idiom is common in Old and Middle English, and remains in rather frequent use in literary Modern English. Thus 1957 Millington-Ward, Peculiarities in English (p. 158) says: “An alternative construction after lest is the subjunctive present in place of both shall and should, e.g. ‘Mary has bought a new mackintosh lest she get wet through again’.”

In recent Pres. D. English constructions with the verb in the main syntactical unit in the preterite and that in the clause in the present are more and more frequently met with. (See 1931 Jesperson, MEG IV p. 162 and 1952 Galinsky 206-7. Cf. § 867 and § 870)

Instances with the modally zero form in the clause opening with lest are:

• c1400 A Deuout Treatyse Called The Tree (ed. Vaissier) 112, 16, ‘absteyne þe from such þingis . . . lest þou shuldist be more sike’.
• 1675 Wycherley, Country Wife (Mermaid) IV, iii, ‘It should be taken from thee, lest thou shouldst do thyself a mischief with it;
• 1695-6 Vanbrugh, Relapse (Mermaid) II, i, ‘a man must endeavour to look wholesome, lest he makes so nauseous a figure in the side-box . . .’;
• 1743 Fielding, Voyage to Lisbon (Everym.) 253, ‘I was afraid of thee, lest thou shouldst have been deprived of that pleasure’;
• 1870 Morris, Earthly Par. I, i, 376, ‘Beware lest . . . in thy mirth, Thou tell’st the story of thy love unseen.’

Visser has many, many, many more examples of all this on pages 867 and 868. You might be able to read those here. If not, here’s one small bit of it:

Notice how in those examples with a preterite in the matrix clause, there is still only a present subjunctive — a bare infinitive — in the lest clause.